> The conservatives viewpoint that the Babylon Bee seems to subscribe to is that gender and sex are they same thing and they are binary. There is no way to debate against that viewpoint. There is no possible compromise position.

No, the conservative position is that sex is objective and factual, while gender is a subjective facet of personality that is socially constructed. The compromise position is to destigmatize gender nonconformance within the category of “man” in a way that does not set up a conflict of rights with women.