In several other forums as well as the news within the last five years or more, there has been significant discussion regarding the separation of church and state. It is, at least in my opinion, somewhat unfortunate that my brethren among the clergy see the need to and diminish this as much as some have done. Besides the fact that each person has the right to follow their own path to the Divine, there is also the protections that are afforded to the church with that separation. Demanding and dictating that this separation become as gauzy as possible does no one any good.
The separation of church and state is/was designed to ensure that 1) no actual state religion occurred that would drive discrimination of or creation of a minority class that did not adhere to the dominant religion. This can be seen within the contexts of the Christian minority in Egypt or the Muslim minority in Italy. This also was supposed to reduce the overall power of the church within the confines of the political arena. The 80’s and creation of the Religious Right kind of set the path for many of the arguments that occur today regarding the aforementioned church/state.
Also 2) that the government would not have a say in the religious doctrine, dogma, scripture, message, practice, non-practice, or overall running of the church. This has, for the most part, been successful barring the inclusion of capitalism in religion (which has been a total failure)
Finally 3) that the church could not be used as a platform for rule free political dialogue/debate. Unfortunately, referencing #1 this has also been somewhat of a less than successful ideal considering the scope of religious entertainers and others who seem to think that they have some say beyond the sociocultural support of the flocks/parishes/groups under their guiding.
As far as the Imam saying a prayer to open Congress, this is, more than anything else, a cultural branding. Anyone who thinks that every Congressman in the room is quietly saying a prayer to God, Allah, Jehovah (which incidentally are all there the same being/creature/manifestation), Buddha, Vishnu, the Green Man, the Human Spark or whatever other form of the Divine you choose is mistaken at best and delusional at worst.
As to the specific call out to the Separation of Church and State, yes, the 1st Amendment says “”Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof …”. Article VI states that “but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.”. The 14th Amendment of Equal Protection Under the Law plays a part as does a list of jurisprudence from the Supreme Court on down.