“At the pool” should be a non-issue.
“In the pool” MAY raise questions because of fluids;
YET, they don’t kick you out of the pool for sweating or peeing in the pool. But they might kick you out for bleeding in the pool.
So there’s a color difference; breast milk is white, blood is red, sweat is clear. Pee is white to yellow but is usually counteracted immediately by properly treated water (which takes into account pee if the levels are right)
BUT I don’t think they should ban, even though the fluids are milky and not clear; the chlorinated water should neutralize most fluids very quickly, so from a public safety standpoint, outside of gawking issues possibly, I can’t see a problem.