Thus the Congressional Chaplain is unconstitutional. Military chaplains likewise unconstitutional. Input from the public square by people of faith unconstitutional. Priests, Pastors and Rabbis in Congress unconstitutional. Catholic Hospitals treating patients at public expense unconstitutional. Jewish homeless shelters housing the homeless at public expense unconstitutional. Chaplains presiding over the dead at their funerals at public military hospitals unconstitutional. Is this your position?
Of course this is not what Santorum was talking about but let's take it to the extreme of your nutty argument.
All are constitutional except your hospital and homeless shelter example. Once these religious institutions start becoming the soldiers of the welfare state, I draw the line.
Those people have no role in the operation of the government.