One aspect of it comes from the notion of collective punishment for the toleration of "immoral" behavior. In the Hebrew Bible, a consistent theme is that entire communities are punished if they tolerate what's considered immoral behavior, so, in that context, what your neighbor is doing is very much your business. You find that idea resurfacing among Puritans in the 1600/1700s.

And some people still believe this. I remember some old guy being interviewed after an earthquake, and he said, "This kind of thing will keep happening if we don't get right with God."

And a misreading of the Sodom story presented a stark example of how God would punish entire cities. (I think that Sodom was about hospitality and the tension between nomadic and urban existence, not homosexuality.)