Each separation of church and State? I was in the impression that the USA was a country that made people sweat on the bible to take a serment, that evocks God in its political speech and discours and even in its moto.
That comment is not sarcastic. I actually feel I miss something to understand the situation.
I don't think so, but people might stare a bit if you do it in a busy place of the park.
I would look for a place with a bit of quiet. I saw people do a variety of things in parks. When they choose a quiet place, I'll assume they want peace for there outside hobby and give them that.