Public defenders don't get to pick our clients. We don't get to pick what kind of cases we get. I take whatever client and whatever conviction comes through my door. I believe that's the only principled way for me to do my job. The presumption of innocence applies to all defendants, no matter how obnoxious or unpleasant. And the constitutional guarantees of due process, etc., apply to all charges. I wouldn't be honoring what I say I believe in if I would turn a client or a type of case away.*
This doesn't mean, though, that you don't sometimes read the details of a case that fell to someone else and think, "I'm glad that one didn't land on my desk."
*unless, of course, a personal conflict develops, in which case the client is better off if I pass the case off to someone else. But I do all I can to avoid those conflicts from developing.