Before I answer, I just want to point out, America isn't one thing. It's a lot of different ideas and individual opinions / often shouting against each other. "Why is this liked in America", it's more accurate to say that there's a movement where part of the US population is making noise about something, not necessarily the entire nation, but a movement. That may be obvious, but I thought I'd point it out.
And I worry that this is an opinion question not a factual one, but I think there's enough agreement behind it to make a good answer.
There's several reasons. I'll touch on a few, and I'm sure I'll miss a few.
1) Unlike many European Nations that have history that goes back millennia, America had a clear beginning, a "birth" if you will and that came from the essentially two documents, the Declaration of Independence and the Constitution. (historians might add Thomas Paine's common sense, which at the time had a huge influence on reaching the public, but it's not retained the sense of importance that the other two documents have). I'll add that the Declaration of Independence, while very important at the time, was a statement, where was the constitution was a design for America. It was the only document that was meant to be used as a design for our government going forward.
2) Going back to the Birth of America, America has founding fathers that are revered even today. Even though Jefferson hasn't looked quite as good in the eyes of history with his sleeping with his slaves, Hamilton, Washington, Ben Franklyn, others, are America's founders and the Constitution is largely their work, though Jefferson wrote it, Washington upheld it was the first president and others had a hand in what it should say. SO 1 and 2 go hand in hand, respected people at the birth of a nation and a document that defends that.
3) It has beautiful language that even opposing parties can agree with.
We the People of the United States, in Order to form a more perfect
Union, establish Justice, insure domestic Tranquility, provide for the
common defense, promote the general Welfare, and secure the Blessings
of Liberty to ourselves and our Posterity, do ordain and establish
this Constitution for the United States of America.
That's practically poetry. The words are easy to like. It's also very high ideals. Everyone wants justice, tranquility, general welfare (I could say a few things about that one). Blessings of Liberty - even though that actually doesn't mean anything specific, it points to a high ideal for a nation.
4) The constitution is a sword. It's a weapon that people can use to defend their rights, even against the US government, and that's true for both sides of the political scale. That defense is even for stuff that not everyone agrees with.
The Social Justice Warrior who wants to defend a protestors rights to burn a flag, can take that right all the way to the supreme court and win, because the constitution defends individual rights, free speech and free expression . . . sometimes to a fault.
The Pornographer is also free to take his case to the supreme court. The constitution defends his right to produce and sell smut, and, I'm not just talking about Larry Flint, but there's a form of political pornography too - Steve Bannon, Alex Jones and Donald Trump sell things that sound good, that have no basis in truth. The liar, the spin doctor, the rabble rouser and the smut peddler can all use the constitution as a rallying cry.
And the small government (and/or anti-government) libertarian can use the constitution to defend his rights and interest. While it didn't hold up in the supreme court, people have argued that the income tax is unconstitutional because it's not specifically mentioned (legally that's a questionable argument), but there is a feeling that the constitution defends the libertarian against an overreaching government (sorry - that's too general). There's also the 2nd amendment that many people feel protects their rights to buy and own guns (it's more complicated than that, but that's another aspect that gun rights advocates love about the constitution).
and finally 5) - covered above, but he Constitution is represents ideas that even people who don't like government can like. "Promote domestic tranquility / general welfare" - Even people who are generally anti-government still want tranquility and general welfare. Maybe not tax and spend welfare, but everyone I know wants general welfare.
So, we have a document that defends the individual's rights on both sides of the scale, a document written at the birth of the nation, and written in beautiful language promoting the highest ideals by people in history that remain popular. There's lots to like.
What changed in the last 15-30 years?
I'll add to that, more recently, in the last 15-20 years or so, there's been kind of an anti government movement in the US, growing in numbers, but these people use the constitution as a way to express what they stand for. "I don't like congress, I'm a constitutionalist" - if a somewhat general statement on my part, represents very deep feelings among many Americans who LOVE America but don't like our government today.
That's the gist of it, that last paragraph especially is why, if anyone says anything anti-constitutional, they get attacked and booed viciously. I've met many people who want to overthrow the government. I've never met anyone who wants to burn the constitution.
All that said, it's become largely an emotional thing. Many who profess to love the constitution, haven't read it, beyond the first paragraph that was read-allowed in grade-school, and, in addition to not reading it, don't understand it.
I want to add that, while these themes are all generally and historically true, the "feeling" of love for the constitution wasn't always there. In the 60s, many radicals who protested didn't hold the constitution in high esteem, and weren't educated in the history. Even though the constitution defended their rights, there wasn't always a reverence for it like there is today. I remember when I was in school in the US (a long time ago) the constitution was a boring document that we had to study. We liked it, but the 70s when I grew up weren't like today. Today, a few decades later, there's a passionate respect and honor for the constitution. People feel it represents them (generally speaking), at a time when there's not much faith in government.
That's a rough summary anyway. I'm not sure it's a good answer, as opposed to my observation, and I'll try to clean it up a bit later and post some examples.