I'm surprised there are banned books with 1st amendment exists in America? I'm curious as to what these are. I think its rather silly that books can be banned.
Purely obscene material is also not protected by the 1st, but since the 1970s, the bar for that has been placed very, very high.
The closest I can think of offhand is that for about a year during the pandemic, Twitter suppressed gratuitous COVID misinformation posts, at the request of the government.