The morality that lies behind the common law of Western Civilizations derives from Judeo-Christian theology, like it or not. It is alluded to many times in the Constiutution and Declaration of Independence.
Ive got news for you, nobody lives in a vacuum. If you expunge "religion" from public life, all your left with is humanitarianism, which is in many ways "religious": Everybody is exactly the same, the goals of society whould be equality of results, evoluted relationships between people are merely social constructs, man can "perfect himself and society", and so on. This is all unsupportable fantasy,and no more (but less) valid than philosophy based on monotheistic religion. You can have a secular society without getting rid of religion from the public sphere.