This issue is so cut a dry
There are only two possible stands to have:
1. Women are so biologically inferior that they need to have their own leagues separate from biological men.
2. Women and men are biologically equal and there shouldn’t be separate leagues for women.
A mentally ill man who believes he is a biological woman doesn’t change either of those choices.
This is kind of a silly discussion, but I want to correct your use of the term "biologically INFERIOR" to describe women compared to men.
Women and men are totally, fundamentally different at the cellular level. Men without women, women without men, ends humanity in a generation.
The phrase "are so biologically DIFFERENT" is better, because using "inferior" in the sports context implies that they should be being measured with the same ruler in the first place - when in fact they shouldn't be being compared, in the competitive sense, at all.
“Women are so biologically inferior”
You didn’t really use that word, did you?
How about physically “Different” instead.
So competition that depends on physical traits could fairly be separate.
You mean there are only two possible stands that make any sense.