Boil it down to it's bare essence and this is simply an argument about indoctrination of children. Liberals believe they should be able to indoctrinate other peoples' kids on any topic at any age with no pushback (and be paid by the taxpayers to do it). And Conservatives believe they (and only they) should control what is taught to their own children regarding sexual orientation (and a multitude of other political divisive topics). Everything else is just talking points, political double speak and posturing.
Liberals want to teach children that being gay (and trans, and every other non-straight sexual proclivity a person might describe themselves as at any given moment) is normal; as early in childhood as possible because the younger a person adopts a belief, the more likely they are to believe it strongly for the rest of their lives. And Conservatives want their childrens' educations on sexual orientation to come from sources they (and only they) deem appropriate.
If you want to understand what is going on, read up on Joe Camel.