Don't mean to put words into their mouths (hands?), but I would have thought that they just mean that generally speaking, people can do what they like if they don't hurt others. Similar to - "The right to swing my fist ends where the other man's nose begins."
Given the context of the threat, it has been said in relation to it.
I honestly haven't got a clue what you're on about. Aside from the fact that it is condescending to the point of being insulting, it's utterly meaningless in the context of this debate.
Unless the irony of dictating how people of a certain lifestyle can live and then going on about 'rights of swinging your arms' is completely lost on you. In which case, right on brotha.