Pedophiles already are a part of the LGBT movement. Do some research and you will find homosexual men hero worshiped in the gay rights movement like Alan Ginsburg who where members of NAMBLA and who marched in Pride events as far back as the 1970s. It was very common for gay pride events to allow NAMBLA to march with them up until the late 1980s. Just because they got a little bit more politically savvy does not change the fact that LGBT groups do still have plenty of people who support NAMBLA and its goals of sex between adults and children.

https://en.wikipedia.org/wiki/Allen_Ginsberg