As is common, you've only addressing the easiest issues.
The point isn't bloodthirsty maniacs, that's just the far end. (Though the number of prominent whackjobs is unfortunately long.)
The point was who is intolerant enough not to want to build bridges with the LGBTQ community. Violence is only the tip of the iceberg. There's various kinds of intimidation. As mentioned, the GOP uses them as their go-to gaybogeymen. (As L, G, and B gain public acceptance, they've turned their focus more directly on T.) Discrimination isn't the exception, it has long been the norm.
What left me gobsmacked was claiming that an intolerant left playing identity politics caused what's happening in Florida. It's like you think history started in the 21st century. You seem quite young, or that just may be the ignoring of history.
The Florida law isn't new, it's just the latest and most aggressive given the shifts in public opinion. The historical precedent is long. It was the norm across the entire society. It's still the norm across the right, or at least they're OK with it given who they vote for.
The short version is that after hundreds of years of brutal oppression, the LGBTQ community is actually starting to raise their voices. Calling the right's reaction a backlash is to completely misuse the word. They are the persecutors and what's happening is a backlash against them. Their counter-reaction is just doubling down on the way they've always behaved.
If I kick a dog every day it's liable to bite me eventually. I don't get to blame the dog, the fault is 100% mine.
What they are doing is essentially beating the dog for biting them instead of taking responsibility for creating the situation in the first place.