You're absolutely right when you point out that "Separation of Church & State" doesn't appear anywhere in the U.S. Constitution. But here's the thing...
Just because something doesn't explicitly appear in the Constitution doesn't mean it's inherently a bad idea. Where we need to be careful is going overboard in one direction or the other, when it comes to any policy. So, when people talk about Separation of Church/State as it applies to public schools: my main objective is to protect students from being indoctrinated with religious text by any faculty member. If students want to run a prayer group on school grounds, or talk about their faith (let's assume it's a Christian denomination) openly in school...I don't view that as a violation of Separation of Church & State. I say this as a proud polytheist/Pagan who receives faith-based flak from pretty much every angle.
Regarding BLM, you could be right that many of its visible leaders espouse a desire to see violence or riots occur. But, again...their nefarious personal agendas don't represent a majority of people who believe in the criminal justice reform measures and other systemic reforms that BlackLivesMatter would like to see implemented. We witness the same thing, so often, with union leaders failing to represent the needs/desires of their actual union membership.
I'm a centrist. I don't automatically get behind a policy just because a liberal politician supports it. But conservative policies have done a number on American democracy, as well. Who wants virtually zero limits on campaign contributions, thus creating an even more bloated lobbyist culture in D.C.? Who prioritizes defense spending on outdated weapons/equipment rather than supporting the needs of military families themselves? Who pushes for laws that ban secular spousal unions (or, alternately, rally for the overturning of them) belonging to same-sex couples? Who pairs life-at-conception laws with a decreased support for contraception? Who selectively targets voting restrictions against areas where voting trends tend to be concentrated in favor of their political opponents? Who pushes for the confirmation of unqualified judges using every rationale of hypocritical mental gymnastics in the book? Conservative Republicans! So don't act as though liberal Democrats are the only ones with dirty hands, here.
