If you compare the history of religious, legal, and moral proscription of gay sex versus the proscription of pedophilic sex, they very much have moved in opposite directions. Anti-pedophile legislation and sentiment is very much a creation of the post-industrial era; a very recent thing in the span of history. A century ago, sodomy could get you jailed or worse, while a twenty- or thirty-something man marrying a fourteen-year-old girl was perfectly normal, and get started on the kids, you two!

Thus, so long as this trend in societal attitudes continues, it's normal that the LGBT community would look down on pedophiles (in the broadest sense of the word; I can't keep track of which words correspond to which age ranges and that nonsense) and not let them come along for the ride of social acceptance. On the other hand, I think it's also… is "unfair" the right word? to some of these people that they are stigmatized for what was, until recently, completely normal behavior, and thus probably still ingrained in the human consciousness to a certain extent. Certainly having consensual sex with a, shall we say, developed teenager should not warrant the same sort of prison sentences and databases we impose on outright rapists and molesters of pre-pubescent children.

(Dear law enforcement: I am not a pedophile and have never committed statutory rape. Go bother someone else.)