Again, I say: Seperation of Church and State. The founding fathers put that in there to keep things like denying rights to people out of this country!
The reason for "Separation of Church and State", as you put it, was to prevent the government from establishing a state church, to prevent the government from taxing churches, and otherwise hindering free religious expression, as was happening in Great Britain at the time. It had absolutely nothing to do with preventing lawmakers from using religious principles to make decisions, or using religious principles as the basis for laws.
The majority of the founding fathers wanted to keep the government out of religion, not ban religion from government. Read and study what they wrote and you can come to no other conclusion. They prayed to God during their meetings. All federal lawmaking sessions, dating back to the Continental Congress, have been opened with prayer.
Some of the founding fathers owned slaves. Unfortunately, they had no problem "denying rights".
EDIT: There was a brief period in the 1850's where the House and Senate did not have Chaplains.