I worked as a life guard and swim instructor at a Y all during college. While we never kicked anyone out for breastfeeding, I wonder if the justification had something to do with a concern about bodily fluids and contamination? If blood, vomit, or poo got in the pool, we had to get everyone out and close the pool to chemically "shock" it. The process took about 12 hours. It was a major pain that made members unhappy. From my experiences, I would guess that it probably wasn't specifically about breast feeding, but the whole (OSHA induced) universal procaution, body fluids thing. I really hope it wasn't just about control and distracted lifeguards.
Guards see EVERYTHING and become pretty de-sensitized to the human body- I hope that the guard wasn't that prude about a boob after seeing old men in tiny little speedos day after day

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I really loved working at the Y and thought they did a great job promoting happy, healthy families. I hate to see them get a bad rap.