You can certainly challenge this rule!  Cryptosporidium is a parasitic infection found in stool, not breastmilk.  And as Morgan stated, saliva, snot, vaginal secretions, urine, and yes, stool and vomit, routinely get into pool water.  That's why they super-chlorinate the water.  If they're going to ban breastfeeders from the side of the pool, then they should also ban people with known (or unknown) pathogens: colds, skin infections, STD's, and late-term pregnant women (in case, God forbid, their water breaks!) and ALL KIDS.  Lets see, that would be about half of all swimmers!  Truly, breastmilk is the least of these worries.
All organisms die when they come in contact with pool chemicals but depending on the concentration in the pool at the moment (inadequate distribution, number of people in the water, sunlight, etc), one can never tell.    You'd be amazed at what can be transmitted through swimming pools, you'd never swim in one again!   And never sit in the puddles on the side!
Annie Brown, FNP, IBCLC
and former lifeguard
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