As we are in the context of trying to restrict access to firearms to people with certain characteristics, I don't think once's religious beliefs is a valid basis to include or exclude.
Its not that you are a different gender, its that you identify with the opposite gender. Its far more complicated than, as you said below, I am Henry the VIII.
The people that went into the Capitol on 1/6 showed a propensity to either actual violence, or to tolerate violence for a political cause. When they did that, IMO they showed far more we should be worried about than this inchoate fear of people who prefer to be the opposite sex. If anyone should not be allowed ot have guns, its the people that went into the Capitol or have posted things in support of Trump calling for death and destruction if he is indicted.
Those are a far better proxy for propensity to violence and should be disarmed first and foremost.
The trans folks say that its not a false reality -- that they identify in another direction. I'm not saying they are right or wrong. I'm just not sure its a mental illness or that it means they might be violent.
The Bible and what you consider under it a "sinful act" is no basis for deciding who should, or should not, have guns.