I think almost every state has laws protecting breastfeeding in public. Otherwise the issue in the US focuses overwhelmingly on parents wanting to prevent children from seeing nudity.

How "public" can saunas get? There are also saunas/hottubs/showers at gyms everywhere. The only restriction is they are single-sex. Mainly for women keeping the guys out. Or at least that was uniformly the requirement until recent politics with transgenders.