A question (primarily for male readers) about mentioning the menstrual cycle in a story:

[alohadave]

If you pee in my kitchen sink, I'm gonna ask you to leave my house. Yes, we all pee. And, yes, it's a normal bodily function. I still don't need to like getting told about it.

There is a difference between peeing in a pool, and peeing into a pool.

One is covert and one is blatant.

 

[YDB95]

One of my four proof-readers (a man) figured that this might be enough to scare off some male readers.

If it does scare them off, then I have no sympathy for them. Half the world has periods, the rest of us can be adults about it.
But to answer your question, I don't think it's likely to scare anyone off.