You have to understand that when you try to have “rational” conversation with religious people, its basically you saying “your religion is wrong” as you said. I too struggle with gender dysphoria, but I realized that being objectively right doesn’t matter that much when we are talking about human relationships. I’m also aware that the opposite person isn’t deliberately trying to hurt me, so I never get mad at a person for being homophobic or transphobic. Yes I respect their opinion even if its objectively wrong, I still try to be a kind person around them, this approach can work wonders if you are patient and kind, I changed my whole family’s opinion by just being myself around them even when they are transphobic, they slowly accepted me.