First things first: The Mosque.
Our freedoms give whomever to build a Mosque/Church wherever. However, human nature has to make us question the motives of someone building a Mosque at Ground Zero. IF, the Muslim world wants to bridge people together and is truly concerned about how they are perceived, this is not the best PR move. If you are wanting equality, love, tolerance, etc., one has to exhibit a hint of what they preach. It's not a one way street.
2: Women in men's locker rooms.
I still don't understand why women are allowed to be in men's locker rooms. One might argue if you do not, that's discrimination. I guess it's discriminating to some extent, but I view it as discriminating between right and wrong. I would also contend that men are not allowed to visit female locker rooms and given the same access as women. How many interviews have you heard of where a male reporter is taking answers from a nude Serena Williams right after a tennis match? It doesn't happen. Is this a double standard? I'll let you make the call.