I'm more exposed to American conservatism. And even here I barely understand it. I used to be Christian, but I left the religion before I realized I was bi, and before I knew genderfluidity and trans people existed.
I guess I'd have to know why individual religious groups, countries, cities,(etc...) have anti-LGBTQ beliefs. Maybe there are no blanket statements that properly address it for the entire world.
The cis-het “nuclear family” with paterfamilias as petty dictator, sex as procreative and pleasurable for the male partner rather than mutually pleasurable is inherently reactionary. Likely quite rare throughout human history too. This idealized version of sexuality stands in opposition to queer expressions of all kinds.
following this, OP could read Leslie Feinberg's Transgender Warriors, there's free copies online, I think you can buy a hardcopy for $14
it's an 'easy' read, and it brings a lot of the Origin Of the Family Private Property and the State, which is was a bit of a slog (though essential reading imo)