What do you base it on that Nolan is a homophobe? He specifically mentioned Brokeback Mountain as part of why he cast Heath Ledger in The Dark Knight.
He (and Bale) repeatedly said that they didn't want a Robin in their movies to avoid comparison with the previous Batman films. It was clear that they feared or disliked any possible homoerotic reading of their movies. And don't tell me about the fake token "Robin" in Dark Knight Rises...