Not that or matters to the sentiment, but men often compete in an open class, not a men's protected class, which is unlike other protected classes like women or disabled.
Yes, I know the Air Bud rule as it applies to non-male athletes in male leagues. And I will say the same as I did elsewhere in this thread- "Black men can't play baseball in the National League" was not a rule. They just made sure any black man until Jackie Robinson knew exactly what would happen to them if they qualified. And that probably didn't include rape threats.
I think it just shows how little they actually value women in any way, shape or form.
They see trans men as a total joke, that they'll never be a "real" man, and of course women would want to be a man! Being a man is the greatest thing ever and only thing these people have going for them, and in effect, transmen affirm their gender identity as being "the best".
It's the same reason they hate transwomen so much. They have such a low view of women, it disgusts them that anyone would willingly lower themselves to that level. It attacks their idea that being a straight white men is the best thing ever, and the idea that maybe it's not, and someone would willingly give up their masculinity and be happier is beyond horrifying to them.