I fully support breastfeeding, and a woman's right to breastfeed her baby, but -
that does not give the mother the right to feed her baby wherever and whenever she pleases.
By the same token, I appreciate potty training, having assisted directly in one lot, and assisted with four others - but that doesn't mean I would appreciate a potty plonked on the table next to me in a restaurant.
I do believe the pendulum has swung too far the other way - a woman's right to breastfeed is not the same as taking it for granted that anywhere and everywhere is appropriate in terms of time or place - and this is the issue.
So no, this woman should not be allowed to breastfeed in a swimming pool, not because breastfeeding is in any way wrong, but because it is not an appropriate place - and we must not lose sight of the fact that however encouraging we want to be, not every place and time is right for every activity, however 'free' we want to be.
I am free to burp, fart, spit and vomit anywhere I choose, but there are times and places where I would not do any of those things willingly - and in the prescence of any other member of the human race is my default position.
All that said, i think the staff handled the issue badly - there is a need for discretion and consideration in these circumstances - a quiet word by a mature female member of staff would have dealt with things far more appropriately.