The christian groups motivated to hate gays are (at least in my experience) the ones most likely to engage in child abuse.
I couldn't find a link to the primary reference, but On Christianity, Fundamentalism, Spanking, and What Constitutes Child Abuse discusses some of the research linking religion and child abuse.
I guess the conservative christians have experience with just how violent, angry, and wretched of parents they are, and since their insane god tells them gays must be worse then them, that's what lets them rationalize the need to "protect" children from gays. At least their advertisements against gay marriage in California, seemed to revolve around if we had gay marriage, children might be exposed to gays.
Speaking as a child raised in a fundamentalist church, why the hell can't we talk about how religion is abusive? Why do the christians get to claim the "moral" high ground of "protecting children". Children bloody well need to be protected from them!