I don't see any evidence of ignorance. His view is penis = man, and vagina = woman, and can we please stop talking about the issue. I understand that mental health research suggests it is healthy for people to live the way they feel inside, but that does not mean his view is ignorant, incorrect, etc, or that he is a bigot for being sick of hearing about the issue.
The problem is, judging somebody solely by what they have between their legs discounts ANY mental or emotional factors in a person. Is that an okay thing to do?
Has science proven what causes someone to be transgender? No. However, some studies seem to show that the brains of transgender people seem to function much more like the genders they identify with, and less like a match to what their bodies are. At some point, we have to decide what is more important in determining who we are as people: our brains or our bodies. We've already decided "brains" is the answer in a lot of cases out there, but some people still aren't willing to accept that for those who are trans.
So, the question is, I suppose, how much proof must exist before we expect people to trust science over their own opinions? (A question also raised in the recent anti-vaccination arguments.)
And the "being sick of hearing about the issue" is a thing you use whenever you're not on the side of the people who are struggling for acceptance or understanding, whatever that social, political, religious, racial, or otherwise topic is.
I mean, do you know how it feels to have people call you a liar, delusional, mentally ill, or otherwise simply for trying to align your life so that you can finally feel like yourself? If that's your opinion, then yeah, it's going to bother me a little.