What Lies Behind Everything, Even the Most Extreme
I think what has to be taken into account, even in a framework of "churn and change", is that the United States of America really is a created, rather than naturally evolved, nation/state/nation-state/country.
That's the first thing. And the second thing, arising out of that, is the foundation myths and national ideals of what this thing called the United States was going to be all about. Even the most radical progressives, in the American context, ultimately derive their notions from the declaration of intent as to what the whole project was based on:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness
And the Constitution, and the laws arising out of it, are derived from the sacred promises:
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
"We have inalienable rights and we were promised justice, liberty, peaceful lives and the common good!" is what lies behind everything, even BLM and whoever else you want to example as the most extreme.
That's what makes America America. A nation of immigrants, willing or unwilling, all bound together under a banner of "you are a human being no matter what your origin, colour, race, religion, sex, gender, or fifty-nine other degrees of breaking this down, and you are entitled to the following", even while the change churns them about in the melting pot/salad bowl/barrel churn.
The extremist progressive, no less than the stolid conservative, both base their appeals to the vision of what the nation should be on these principles. Maybe the progressive believes it should be a pansexual panromantic nonbinary polyamorous luxury gay space communism cottagecore collective, but that arises out of the ideals of peaceful lives, justice, and the general welfare based on equality, liberty, and the pursuit of happiness, and that nobody is entitled to interfere with eir rights and the exercise of same. And those foundational principles are what everyone wants to conserve, even if they don't speak of it in that fashion.