As I see it, they get plenty of respect when they get their turn to say their prayer in public; that is way more respect than a Christian or Jew will get in a Muslim nation. Therefore, the U.S. maintains the high standard, while the Muslim nations enforce their Islamic religion at the point of a sword.
However, my standing and/or bowing my head in deference to their god while they pray their public prayer would be tantamount to renouncing the One who I know to be the True God. Heaven help me if I ever do anything less than leave the room in that situation.
Any Muslims in the crowd are more than welcome to walk out of the room when a Christian or Jew prays, too. It shouldn't bother us one bit. Anyone who's "offended" by non-believers leaving the room when he prays is just looking for a reason to be offended.