There are actual women who are happily want to be addressed as Alex.

True enough, I didn't choose the best example male name. This seems about as relevant to anything else I was saying as the fact that "women who are happily want to be addressed as Alex" is ungrammatical is to anything else you are saying. I should have said "Alexander" or "Adam" or "Alfred" or something.

Doing differently takes mental filtering. That carries a cognitive cost.

Sure. Did I ever claim otherwise?

Suppose you meet someone who looks male to you. It turns out that actually the person is a woman, with two X chromosomes and a uterus and all. I'm guessing that once you discover that you'll refer to that person as "she" despite the small cognitive cost of doing so, and it probably won't even occur to you to think it an unreasonable imposition to be expected to do that. And the chances are that, actually, you won't insist on inspecting her chromosomes and reproductive organs before adopting the appropriate pronoun.

If your attitude is different in the case where a near-identical-looking person has XY chromosomes and was called "Alfred" when born but now goes by the name of Angela and considers herself to be female, even though the cognitive cost is exactly the same in the two cases, then I suggest that the cognitive cost is not the real objection.

I don't think anybody should be laughed at for wearing a dress

Neither do I, but apparently some people do.