I don't think in general that this is much of a factor. They're giving wildly false impressions about what the left is about, not actually creating the craziness.I think Trump appeals to many people because he makes them feel relieved from their fears and insecurities. It isn't a real relief but on an emotional level it is there for some reason
I wouldn't be surprised if a lot of the trans and woke stuff is actually being funded by conservatives behind the scenes to put the Democrats in a bind. They want to be the empathetic all inclusive party but so much of the general public including Democratic votes think a lot of trans and woke stuff is crazy.
However, I have long suspected that Antifa is somehow funded by the right.