It seems that both the Republican and Democratic parties look at the appointment of a Supreme Court Justice as a political move. Optimally, a judge has no part in politics. Their personal opinion should not come into play at all - instead it should simply be about what the law is in a particular case.
How political parties view things is not necessarily commensurate with reality. After all, they have a political agenda to push. In this case the view of (federal) judges—Supreme Court Justices or otherwise—as dyed-in-the-wool partisans is not really borne out by the reality. The type of 5-4 split decisions that attract so much attention are in fact a small fraction of the decisions made by SCOTUS, most of which are unanimous or have only one or two dissents, and odd bedfellows of so-called "super liberal" Justices joining with "super conservatives". And it tends to be notoriously difficult to predict how a federal judge, a Justice in particular, is going to rule on things after their appointment.
Justice David Souter was nominated by a Pro-Life Republican President (the first George Bush), was expected to be a solid conservative, and ended up being seen as one of the most liberal, Pro-Choice justices in recent history. And recently we had Justice Gorsuch, who had been touted by Trump as a sure thing for Conservatives, joining a ruling that sex discrimination statutes covered sexual orientation/identification, with the "but-for" test. Which is not to say that Gorsuch hasn't shown an apparent conservative-friendly lean on many cases, but it nevertheless was something of a surprise that the assumed 5-4 "conservative majority" at the time failed to coalesce on an issue that seemed so definitively a Conservative versus Liberal one.
Some tout this as a positive feature of the lifetime appointments all federal judges (including SCOTUS Justices) receive, arguing that because they are freed of political and career pressures they can simply follow and apply the law and constitution in a pure, unobstructed way, unfettered by consequences.
What Justices and (most) Judges do have is a judicial philosophy: a view of how the Constitution and laws are to be interpreted and applied. And certain judicial philosophies are more amenable to conservative or liberal politics. "Originalism" is, pretty much by definitions, quite agreeable to conservative politics, as it basically says "Let's keep doing things the way we used to and have already been doing them". And this sort of judicial philosophy became heavily popularized by the late Justice Scalia, and Trump appointees to SCOTUS have all had strong connections to this philosophy.
Historically speaking, SCOTUS has pretty much always been viewed by Americans as the most apolitical, trustworthy, and ultimately-on-their-side-of-things Governmental institution or branch. Which is a little odd in some ways, because most attempts to measure how "liberal" or "conservative" a given SCOTUS is tends to come to the conclusion that most of them are heavily conservative, and the current Roberts court (pre Scalia's death) was actually a bit left of the historical norm, but still notably conservative. Modern perceptions are perhaps twisted by the lingering memories of the Warren court from the 50's and 60's, which is often considered the most liberal court in US history.
But the entanglement of SCOTUS with politics was almost immediate. Early in the history the court seemed deeply wary of such entanglements, and mostly avoided doing anything significant that might rock the boat, for fear of endangering the young nation. President Washington tried almost immediately to get the Justices to offer him advisory legal opinions on potential laws and actions, and he was kindly turned down (on the basis of the "Cases or Controversies" clause, which the court considered to bar them from such opinions).
Marbury v. Madison, in 1803, was the first time the court ruled on whether acts and actions of the other branches were "constitutional" or not, and in particular asserted that such determinations were a power belonging to it, and they could use it to nullify acts of Congress as well as compel certain members of the Executive to perform certain actions. Now this is quite significant, and the ruling ultimately a masterpiece in retaining that evasive "don't rock the boat" directive despite it being a ground breaking ruling.
The evasion bit arises because, while it declared that a certain act of Congress was unconstitutional, and that the court had the power to compel certain members of the Executive branch to do things, it did not actually do either of those things. The law in question had already been repealed by Congress (though it was in force at the time of the issues at hand in the case), and the court used this Constitutional invalidity to declare itself lacking jurisdiction on the case, and so didn't order anyone to do anything on said technicality (but it did go out of its way to assert that it could, otherwise).
And all of this was necessary because then-President Jefferson was very adversarial toward the court (as was Congress), and was of the opinion that the decision of what is and is not constitutional belonged to him, the President. A ruling which attempted to order him to do anything was, in all likelihood, going to be ignored, and we'd enter into a major constitutional crisis. By declaring they had these powers, but using a (somewhat contrived) technicality to avoid actually using them, SCOTUS robbed Jefferson and Congress of anything substantive to actually gripe about. For in fact Jefferson got what he wanted—to not be told by the court what he/his subordinates must do, especially when it concerned an act from the end of the preceding President's term—and Congress got what they wanted—to not have the courts invalidate one of their laws without their involvement. And SCOTUS got to walk away with powers that not everyone agreed they had before that point.
For a more modern flash point, there is really no more important case to look at than Roe v. Wade, which occurred in 1973, under the Burger court that followed the Warren court. This decision took an issue—abortion—that had to that point been a strictly local, state-level one, and transformed it into a national one. Now the only way that those who disagreed with the ruling could do anything about it was to operate on the national stage, and they would have to go through one of two very difficult routes: amend the constitution or somehow reshape the court and get it to change its mind. National politics was dramatically changed as a result. And ever since, every single SCOTUS nominee has lived under the shadow of that ruling, and every hearing infected by it: Liberals want to know if a Justice will uphold it, and Conservatives want to know if a Justice will overturn it. Even Justices that got confirmed with massive majorities, like Ginsburg and Sotomayor, were grilled on their Roe v. Wade stance. They all generally avoided it. That the court, while often rolling it back inch-wise, never overturned it, despite acquisitions of Republican appointed Justices (such as Souter and O'Connor) and apparent "Conservative majorities", has become a major frustration to many conservatives. While there is more to Conservative vs. Liberal politics than just the issue of abortion, it's unquestionably a major force, and that Roe v. Wade resulted in a massive, national-scale transformation of politics, and overall outlook on SCOTUS.
The other answers point to more distant historical events, but it's probably more germane to highlight the most recent change that has significantly increased the polarisation of the US Supreme court.
In 2017 the Republican party removed the filibuster rules from Senate procedures around the approval of supreme court justices. This is the so-called Nuclear Option.
On April 6, 2017, Senate Republicans invoked the nuclear option to remove the Supreme Court exception created in 2013. This was after Senate Democrats filibustered the nomination of Neil Gorsuch to the Supreme Court of the United States, after the Senate Republicans had previously refused to take up Merrick Garland's nomination by President Obama in 2016.
Prior to this change Supreme court justices required at least some form of cross part support and indeed many appointments had wide spread support from both parties in the Senate. Justice Ginsberg was appointed on a 96-3 vote despite her liberal credentials.
It is the lack of need for cross party support that has dramatically increased the politicisation of the court.
Historically, when did the Supreme Court begin to be a political body?
March 1803, when Outgoing President John Adams appointed several dozen supporters to federal office 2 days before incoming President Jefferson took his oath. The Senate approved Adams nominees including federal judges. When Jefferson took office a handful of the commissions had not been delivered. Jefferson instructed his Secretary of State James Madison not to deliver the commissions still outstanding. One of the candidates sued for his commission, William Marbury. Thus the principle of judicial review was born elevating the role of the court and forever politicizing it.
What makes a judge a Democrat or Republican? It can't just be their personal opinion - they have to be backed by the law.
It doesn’t really work like that, the constitution is more than 200 years old and only got through the ratification process by choosing words opposing positions could both claim supported their views.
Applying the constitution regardless of political beliefs require interpretation and the interpretations just don’t always agree.
Interpretation is how conservatives turn the second amendment
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
Into every man, woman and child has a constitutional right to buy as many guns of unlimited models devoid of regulations. I’m not saying the second amendment doesn’t support their position I’m saying it doesn’t without interpretation.
It’s impossible to apply the constitution without interpreting it. Literalists just interpret it differently.
As for Democrat and Republican judges, that’s fairly irrelevant too. Some of the most aggressive “liberal” judges have been Republican nominations.
You never know how a judge will vote when he gets on the court.
The Supreme Court and its Justices were never meant to be 'apolitical' in the narrow sense of the term. That much should be obvious from position of SCOTUS as check-and-balance on the other expressly political branches of the government. Justices — and in fact all members of the Judiciary — are tasked with interpreting the abstract principles of written law and the constitution, and that act of 'interpretation' means Justices will necessarily draw on their own understandings of what it right, wrong, appropriate, inappropriate, important, or trivial for the nation as a whole. Those understandings are the heart of a political orientation, and a Justice who lacked them entirely would be incapable of adjudicating anything.
The Supreme Court was meant to be judicious: an elite panel who would argue the pros and cons of the various cases laid before it, to find a resolution which is:
In other words, the Supreme Court was meant to take on an unconscionable mess — the conflicting mass of laws and policies enacted by federal, state, and local legislatures and agencies; the wide assortment of disparate rulings from hundreds or thousands of lower court judges; the sometimes rabid attempts of different groups to push through political or legal agendas — and make sense of it, so that US law is reasonably clear, consistent, and coherent across the board. Justices are appointed for life to remove them from political pressure, yes, but not specifically so they can be apolitical. Justices are appointed for life for the same reason that college professors are given tenure: so that they can hold sound, informed, sophisticated positions of reason, even when those positions tick a lot of people off.
Justices are Republican or Democrat (or conservative or liberal, or even Marxist if it came to that) according to their own inclinations and desires. Justices vote just like the rest of us, and what they do in the voting booth stays in the voting booth. Their political leanings clearly inform their legal opinions, of course, and that's fine so long as their legal opinions are reasoned and comprehensive. For example, I've read several of the late Justice Scalia's opinions, and while I strongly disagree with many of his interpretations and beliefs, what is clear is that Scalia had a profound mind. His arguments were good; his reasoning was sound. The same goes for most of the SCOTUS Justices (notable the late Justice Ginsberg who was an equally profound thinker, which explains her long friendship with Scalia). There is always room for reasoned intellectual disagreement of that sort; I might even go so far as to say that the point of the Supreme Court is to take these broad, inchoate political biases and force them through the wringer of critical reason, squeezing out what is irrational and heated, and leaving what's left to be examined in the cool light of day.
We only see problems in the court when a Justice is appointed who puts politics ahead of reason. For instance, we could look at Justice Thomas, who rarely asks question, argues points, or offers opinions, and who generally acts as a mere rubber stamp for conservative political postures. 'Rubber stamping' of that sort violates the very spirit of the Court, and undercuts its institutional obligation to discursive reason. The current worry is that the Trump nominees for the Supreme Court were chosen more for their partisan loyalty to particular political agendas than for their intellectual abilities; both Kavanaugh and Barrett are comparatively young and inexperienced, and neither has a proven track-record of judicial accomplishment that would demonstrate their capacity for reasoned argumentation. I'm not suggesting that either is dumb by conventional standards — obviously not — but the intellectual bar set for Supreme Court Justices should be extraordinarily high. The application of that sophisticated form of reason is the only thing that keeps implicit political biases in check; without it, the court may as well be an extension of whatever political party manages to grab control of it.
Let's not forget that the first Chief Justice, John Jay, was extremely political. He actually ran for governor of New York while he was sitting on the Supreme Court. And also while he was on the Supreme Court he negotiated the Jay treaty, which had nothing to do with his duties as a justice and was very, very controversial. Having been a co-author of the Federalist Papers, he was unquestionably aligned with one party, the Federalists, against the Democratic-Republicans.
