My point is that the Constituion establishes the right of all to compete. The gov't can't say "You must be a Christian" or "You must be baptized" or things like that. But it does not ban politcal activism while Christian either. Religious people have just as much right to persuade the public of the rightness of their political ideas and the wrongness of other ideas (barring only things like sacraments, church membership and things like that) as anyone else.
Thus people from various faiths or no faith at all can find themselves on the same side politically, joined only by values and political philosophy. Faith and morality are guides, not mandates. What is mandated is only the right of all to compete in the persuasion/debate process. No one's faith is established, but the general, structural morality of the majority is put into law (I say this because many moral issues are of the lower kind, where culture has its own way of stigmatizing behavior without actually making it illegal. A person is motivated to not behave a certain way because it brings public embarrassment.)
Also, God can be honored anywhere and at all times, including in gov't. Our political oaths are taken in His name; our rights come from Him alone; in freedom we answer to Him alone; why would a gov't such as ours want or need to dishonor Him? That's an important principle.
The constitutional prohibition on test oaths basically spelled the end of federalism, and asserted America's destiny as a French-style secular republic. Note the depressing progression:
Once upon a time, civic office was reserved for confessing Christians who recognized a transcendant power beyond their own ambitions.