In theory the judges are meant to be independent of politics. In reality this is not achievable; every judge is a citizen and has their own political beliefs. This situation is worsened because those beliefs are generally fairly public and politicians choose judges (especially for the Supreme Court) whose beliefs align with their own, in the hope that this will lead to court judgements that align with their policies.
At the lower levels of the judiciary this tends not to matter so much; the laws are detailed and are either reasonably current or have plenty of precedents from higher courts. However by the time you get up to the US Supreme Court the judges are not just judging the facts against the law, they are also judging laws against the constitution. This is inherently political for two reasons:
The Constitution was written over 200 years ago. Since then the USA has gone through civil war, the abolition of slavery, an industrial revolution, de-industrialisation, and now an information revolution. We have powers that the Founders could not imagine. We also have problems and limitations that they could not imagine either.
The constitution is a very brief document. Including amendments and signatures its got 7,591 words. The Bill of Rights, where most of the really contentious stuff lives, is about 500 words. By contrast the Patriot Act contains about 59,000 words, and its not unusually long as laws go.
These two facts mean that over the last 200 years the Supreme Court has had to "discover" or "invent" (depending on your view) a lot of extra stuff that the Framers didn't think to include.
For instance, the First Amendment prohibits any law "abridging the freedom of speech, or of the press", which is pretty categorical. But at various times the Supreme Court has agreed that the government can make laws abridging freedom of speech. They apply "strict scrutiny", but that phrase isn't in the constitution: the Supreme Court invented it in 1938. You could argue that these decisions were wrong and the plain meaning of the words should rule, but you'll be arguing for the legalization of child porn if you do.
Another area is the Commerce Clause, which says that the government has the power "[t]o regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes". Those 16 words have been interpreted with increasing breadth over the following two centuries, until today any activity with even the most trivial economic impact (such as growing your own wheat, or weed) is held to be subject to federal jurisdiction owing to its effect on interstate commerce. Again, you could argue that this is wrong, but vast slabs of USA law now rest upon this interpretation.
That is just two examples. There are many others.
All of these decisions are political, both in the sense that they directly intersect with the concerns of politicians, and in the sense that they are not soluble by simply reading the words of the constitution so the judges have to apply their personal political beliefs about what the Right Thing is. In doing so they unavoidably leave the domain of legal interpretation and enter the domain of politics.