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 theory, I believe, is that the nuclear family is very useful to capitalism because it breaks the bonds which form larger communities. If your family is the largest social group (outside of the nation itself) that you are part of, the largest group in which you are expected to protect other members and vice-versa, it becomes very difficult to organize and easy to see everything as a competition mediated by the market. Additionally, the patriarch dominates social reproduction, protecting his position of power by attempting to reproduce his ideology in his offspring. At the same time he is weakened in greater society due to his alienation from both his peers and his own family.
Basically it carves humanity up into small cells which are inherently desperate and alienated, making solidarity almost impossible.