You can't change someone's mind with facts and logic if facts and logic weren't used to make up their mind in the first place.

You also can't change someone's mind about any given topic if their stance on that topic is part of their identity. To a conservative, their very core identity/belief is that everyone is made "by God" exactly the way they're supposed to be. Before you could get them to believe that something like gender dysphoria is real you'd first have to make them believe that their religion is wrong.