Bans often rely on the obscenity exception to the 1st Amendment:
https://constitution.findlaw.com/amendment1/first-amendment-limits--obscenity.html
SCOTUS has never given a clear, well-defined, repeatable test to say exactly what "obscenity" even means, so local jurisdictions are free to push the envelope.
If that sounds like a pile of bullshit waiting to be exploited, yes, and that's exactly why we're seeing this happening.
Also PETA got involved, because they've never seen an animal-centric story they couldn't weasel themselves into.