To be fair, they have a problem with trans women in women’s sports. They don’t have a problem with trans men in men’s sports because they can’t imagine a situation where a trans man could possibly compete with “real” men.

It goes along with their idea that women are weak, so women are weak athletes and women’s sports teams are weak. If you accept that, it’s not a big stretch to think that someone who has gone through puberty as a male will have an automatic huge advantage in every women’s sport because their body has male characteristics.

On the other hand to them, the military is the ultimate in manly activities. Anybody other than a pure, manly man will be at a disadvantage in anything military. That includes trans men, trans women and regular women. Right now the focus is on trans people, but I’m sure they’ll want to kick women out of the military too eventually.

So, if you accept that logic, it makes sense that trans women are too weak for the military, but too strong for women’s sports. There’s no contradiction there.