I see the point you’re trying to make but I question the relevance of Fu Yuanhui’s statement to your argument.
Personally, I wouldn’t want to swim in a pool in which women have been bleeding for precisely the same reasons that I wouldn’t want to swim in a pool in which men have been urinating.
This has nothing to do with myth and folklore and squeamishness and it has nothing to do with menstruation. This is simply because blood and urine, while both are sterile at the instant that they leave the body, like most bodily fluids, do not belong in a shared swimming pool.
If a person of any gender, featuring any possible corporreal arrangement of genitalia, arrived at the pool-side with a cut on their leg from which blood was actively flowing, should they be allowed to swim? I think not.
You argue against the stigma surrounding menstruation and, in that cause, you have my full support. I simply do not believe that Fu drop-kicked any theories or made a valid stand against it.
Update: I should clarify that I have no qualms about women swimming during their period in private swimming pools or, with a tampon or other such device, in public pools.