Yes, I do believe that certain books that are banned should not be allowed in public libraries or schools. I believe this strongly because it puts bad images into little kids minds, and when kids read certain material, they want to act it out or try to become that certain individual if they really appreciated and liked the book. In some of these books, there is overthrowing the government, killing of little children, racism, and same sex couples getting married. No way in hell would I let my kids (if I had any right now) read about these things happening because it puts ideas in their heads, and you never know with society today what kids are capable of, or what kids want to try. Yes, maybe they are well written books and interesting, but keep them out of the reach of kids, and the only way to do this is to ban the books from the public libraries and schools. If you want your kids to read a certain book that has been banned from public libraries, then go and get the book for them personally.
Right off the top of my head I cannot think of any texts that should be banned from public libraries or public schools. I can say though that certain materials such as books with racist comments, adults sexually harassing kids, adults beating on or murdering kids, raping, devil worshipping, overthrowing the government, and basically anything that kids should not read about or hear about until they are old enough to be mature and choose if they really want to read it or not.
To me, yes and no, is my answer to the question of does banning of books violate our first amendment rights. I believe yes because we do have freedom of speech, which virtually means you can say, publish, or express yourself in almost anyway you want too even if the people around you disagree 100%. On the other hand though there are boundaries and a lot of these banned books have obviously crossed the line. You cannot make bomb threats, death threats, or verbally abuse and threaten anyone in anyway without getting in serious trouble.