To me, you are using different sets of criteria for your argument.
On the one hand, you are saying a deductive argument for beliefs cannot be made, without distinguishing what those beliefs actually are. Transgenderism could be considered a belief, just as Christians believe that Jesus Christ rose from the dead. Both beliefs defy what we scientifically understand about our physical world.
If we are to make our logical arguments using specifics, such as with transgenders, then the consistent thing to do would be to say that a deductive argument disproving the existence of God/Jesus can in fact be equally made.
I may be wrong, but it seems like you are using an argument that a belief in God is not contradictory using a metaphysical approach, which, by definition, is "abstract theory or talk with no basis in reality." It occurs to me that transgender could also be interpreted metaphysically, which reduces our disagreement to recognizing that either there is a contradiction in believing in things that lie outside of our physical reality (and the words we use to describe it), or there isn't.