I understand their point--a capitol is typically extremely formal. If I had a child with me, I wouldn't feed him/her in the hallways (or the bathrooms), and would find a spot in the cafeteria or outside on the steps to give him/her a snack. If I had a bottle-feeding infant with me, I would do the same thing. I think if I brought my nursing infant with me, I would find an extremely secluded spot for feeding him/her--not a bathroom, but certainly a spot where food is acceptable--the cafeteria, a bench outside, the office of my incredibly supportive delegate, etc.
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It wouldn't be because nursing a child in public is inappropriate, but because eating in most parts of the building is inappropriate. Also, if I were wearing a suit--as I would for a legislative hearing, I would need a more secluded spot for nursing because my clothing would be less likely to be nursing compatible.
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honestly, if I were attending a legislative hearing, I would pump and leave him/her with a sitter for the time I was in the hearing. I nursed my child until he was 3 and a half, and I NIPed regularly until he was over 2 years old--but I still think there are times and places it is not appropriate, even if it is legal. If I wouldn't feel comfortable eating in a location or feeding a toddler in that same area, I wouldn't nurse an infant there.
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the only exception to that would be if I were representing a breastfeeding or parenting coalition, and they specifically wanted nurslings there.