As soon as you start calling people MRA activists you lose some strength in your arguments. Same as handmaiden.
I disagree. Naming is a powerful action and often cuts through the nonsense. In this sports debate, it's not the rights of females identifying as trans who are the issue. They can compete, no one cares because even doped up on testosterone, they are not competitive against men. The best example worldwide trotted out regularly managed to win a couple of races competing against males but never got anywhere with it.
The reverse is not true. Now that the first cohort of males who identify as trans are breaking world records and taking gold medals, it is becoming increasingly clear that females will be adversely affected when their sports are opened up to males.
You have therefore a juxtaposition of our right to fairness in sport vs the males' need for validation by competing in the sex class they wish to emulate. Women's right vs men's privilege. If you advocate for the latter and against the former, you're a men's rights activist. Doesn't matter that you're only advocating for a limited set of men.
I find the word MRA fitting under the circumstances.