"Saying that gender does not exist, is like saying that love does not exist or enthusiasm or happiness or the thrill of being alive do not exist."
This insightful observation may be the core of the issue. At the current state of scientific inquiry, the objective existence of gender -- which is essential to the objective existence of being transgender -- is not demonstrable; but that doesn't mean it isn't real. It simply means that it is an intangible, like love.
I make this point frequently when talking to social conservatives. Some of the most important realities in our lives are intangible.
But there is a political downside to viewing gender this way. If we can't prove it exists, then it's a matter of belief; and matters of belief upon which there is significant lack of public consensus are not a suitable basis for a civil rights movement. That would lead many trans people to reject this view of gender, but framing reality to serve an agenda is no way to seek truth. And if we are seeking truth, about ourselves or anything else, we must be willing to take the sulphur along with the molasses.