I know for a fact there are animal cruelty laws on the books in many jurisdictions. If you go to the cops and courts and say, "but it's part of my religion, we do animal sacrifice" you then are at the mercy of the courts to decide which law takes precedence. the Constititional law saying the government shall not interfere with the establishment of any religion, or, the ability of states and local jurisdictions to enact laws regulating what citizens can and cannot do. If any given Constitutional clause or amendment was somehow always and without exception enforced, US society would be very different because individuals could make excuses left and right to excuse otherwise illegal behaviors as being protected by the Constitution. That doesn't happen. Therefore no provision (or most of them anyway) is absolute, either in a literal sense or in spirit. Heck look at the clause that says Congress must declare war -- yet the government has engaged in hundreds of military adventures across the world, without a declaration of war ever being made or even requested, by the Executive branch. The Constitution is truly "just words on paper" and the government effectively just does whatever it can get away with. That's what the historical record suggests anyway.
I am not debating the fact that the Constitution as interpreted is not the Constitution as written.
However you made a very specific claim that flies in the face of what I understand the interpretation to be. I would be interested in a citation. (I've already given a citation of the Supreme Court ruling in favor of animal sacrifice on grounds of religious freedom.)