Well this is an excellent question, isn't it?
Why those books?
I think it's pretty obvious why they want to ban the Handmaid's Tale. It's a stark warning about the kind of society you can end up with once you start trying to control women by limiting their reproductive rights.
As for Tom Sawyer, well, that's an interesting one. It's one of the most banned books in history, both by the left and the right, for multiple reasons ranging from "questionable morals" to the use of racial slurs. I would be no more surprised if Democrats wanted to ban it. Disney has even removed some of its own content from Disney+ and put trigger warnings on a whole bunch of other stuff for the use of harmful stereotypes which wouldn't be acceptable now. For what it's worth, I haven't seen Song of the South (which was removed) but I think keeping films like Peter Pan and Dumbo available with a trigger warning at the beginning is probably the right approach.
I genuinely don't know quite where I stand on the issue of school library books, because whilst I don't agree with book banning in general, there clearly are books which are completely unsuitable for children. The problem is, who gets to decide what is suitable for children and what isn't? There are some books written for children which I personally think are unsuitable for children or even dangerous, for example, there is one which I think encourages girls who are struggling with their gender identity to hate their bodies and want to use a binder and have a mastectomy. I'd go ape shit if I found that in my child's bedroom, and yet, who makes the rules about what is suitable for children and what isn't? I don't think there is an easy answer.