Librarians are generally quite opposed to banning books and I haven't seen any sign that this is different: some large systems (e.g. NYPL) have said they're keeping them in the general collection and others (e.g. Chicago) have said that they're temporarily removing them from circulation while deciding what to do long-term. I would bet that the major of local decisions will end up being along the lines of either not shelving them in the children's section or having some kind of contextual note for people who request it.
It's easy for Chicago to say that they're figuring out what to do long term, but somehow these books were all fine (and in the children's section!) for something like 70 years, and now they're suddenly radioactive.
What this suggests to me is that there has been a shift in values among librarians, and when the publisher made the decision to take them out of print, this forced a reevaluation, and then we discovered that avoiding any whiff of racism is a more important value than free speech. I think that's really sad and depressing.
It's actually the libraries pulling them from the shelves that seems so bizarre to me. I could understand them moving them from the children's section to somewhere else, but to remove them from circulation entirely, and then presumably put a bunch of other books out on the table for banned books week is just strange.
Public libraries have historically been a big institutional force for the rights of free speech and free thought, fighting in court to be able to loan out (and keep secret the names of borrowers) very controversial books. I honestly cannot understand sacrificing those principles and all of that history over Dr. Seuss.