I would say absolutely no (at least for public schools). However, I do believe schools should not carry books that are of an MA (Mature) rating as these have been deemed by a third party to be inappropriate for children and mostly due to sexual content or extreme violence. I know that the system can be abused, but I would say that it does not have evidence of that being an issue and has enough checks and balances to avoid most problems.
I do also believe that parents should be able to censor their kids' books. I would not do this myself, but I do believe in parental rights. There are also enough technologies and databases around today that it should be easy to implement a system where parents can restrict their children from renting out let's say religious books or a particular author. We are more than capable of scanning a book code with the student ID and getting a "Sorry, your parents don't want you to rent this".
In general, no. There are exceptions to the rule where age appropriateness and maybe some other qualifiers should be up to the librarian's discretion to some degree. I'd also like to see more schools/teachers embracing more thorough book discussions where students can get a good diverse understanding around how to critically analyze novels and stories.
No, school libraries should not be censoring books. The only books that should be censored are ones that are mature like romance novels, but no school library is going to carry books like that. (I would hope not at least.) Do parents have the right to prevent their children from seeing certain books? Absolutely, so perhaps there could be a system put into place for parents to block certain books being checked out of the library.
Do I think that grade school libraries should have books promoting things like Nazism, porn, or propaganda? No, absolutely not. Should books that educate about those topics, while showing why they're bad be allowed in schools? Absolutely. Schools shouldn't censor things that are considered "controversial" just because that's what they were, but we also shouldn't allow obvious propaganda into grade school libraries in the name of free speech.