Adding phrases like "separation of church and state" implies things neither in the Constitution nor intended by the founders. I know some courts have chosen to read it differently but the reality is the constitution does not give the courts the right to intrepid new meaning into the Constitution. They granted themselves that power despite the fact that it is clearly prohibited.they were trying to prevent the government from doing what England had done and establishing a official church not forbidding local governments from opening city council meetings

It is very clear from reading the correspondence from that time with a prayer.

As a libertarian I firmly support the idea that government should not be involved in religion but that doesn't mean I think we should denying football players the right to pray before a game and have their coach lead it if he chooses. That in my opinion is government interfering with religion. Let people pray or not as choose even if they are on government property or they are part of the government. The idea that government should go out of its way to recognize less popular religions I think it a bigger problem. The real issue comes not when employees of the government practice their religion but when the government uses its power to influence religion saying who and when religious expression should be allowed. There should be limits, I don't want my children indoctrinated at school but saying "under God" doesn't really cross that line.