Why do they all kill each other in the name of God if he is the same God??
It is a convenient emotionally charged subject. Far easier to get people whipped up into a frenzy to kill infidels than tell them that the King of England wants the prestige of conquering the holy land, for example. Another example would be the teenage homicide bombers that promote the agenda of evil men in the name of Allah. Also, if it is a faith based argument then no real evidence is needed. You simply have a man of the cloth proclaim your enemy and God given duty and off you go to kill someone.
The point of the constitution is to protect the government from being ruled by a religion AND to prevent a religion from being ruled by a government. It was not meant to take God out of our society.
As was mentioned, several religions have found themselves persecuted by the government of the USA anyway. At first it was specific groups, and now it has made its way to Christianity in general. The liberal judges that are handpicked to sit in on cases that allow a single student to remove religiously toned music from school choirs or a person to remove the ten commandment statue from a courthouse know what the ammendment is for, but they also know that they can promote their own "State as God (or supreme nanny)" agenda in this role.