Don't do that. Their end-game isn't to move the books. It's to identify the books so that they can be banned in some direct way. Next they'll demand that the library keep track of how much money they spend on LGBTQ books and spend an equal amount of money on anti-LGBTQ hate books. They'll demand that kids get parental permission before they can look at those books. They'll challenge every single book and make the library staff spend a lot of time fighting the challenges. You can't give in to these people and hope they'll move on. They won't move on. You have to fight them.

Ooof. I have not dealt with this personally, although I suspect that it's coming given what our state legislature is up to, but have you checked out the American Library Association's page about how to deal with censorship efforts? It may have some relevant advice even if you're not in the U.S.

Sometimes I wander around and pick up whatever looks interesting, but often that gets overwhelming, and then I pick books out in advance, use the online catalog system to put them on hold, and pick them up from the hold shelf. That way I can consult my TBR list, check and see what's available, and choose a book from the comfort of my own couch.

I keep a list of interesting-sounding books that I want to read, which helps with this process. I use reviews, recommendations from friends, things I read on social media and hear about on podcasts, etc. to make my list. If the "blind date with a book" event worked well for you, I would see if the library has recommendations or book lists on their websites. Sometimes the individual library staff members recommend books, and you can figure out whose taste tends to jibe with yours.