Drag is an adult performance show, On par I guess with burlesque. Would the library be happy for a scantily clad, heavily made up woman to be reading to kids with her crotch visible. If not, why does the drag thing make it appropriate?
If anything, I think it could give entirely the wrong impression about gay and trans people - similar to the excessively camp gay characters and stereotypes in older sitcoms.
Presumably gay men do not want to be characterised in that way (I’d imagine just being a person/dad living their life like anyone else) and despite the “trans umbrella” thing, I’d imagine most trans women want to be taken seriously as a normal member of society, not these cartoonish characters. And as others have said, the obsession with drag queens and nobody else is hardly diverse.
That’s before you even come to the blurring of boundaries, misogyny and inappropriate social media content (which imo should be completely separate to anything they do with kids - different name etc).
From what I’ve heard of them, the DQ makes it more about them than the story they read. A good storyteller should be able to hold attention with their words.
I actually think the DQ is just a gimmick to get the parents in (whether they think it’s fun or edgy, whatever) like the man dressed as Ronald Macdonald for a Macdonald party in the 80s - I never liked those either - anything with men dressed up, hiding their real appearance behind a mask. Always gave me the creeps.