I won't argue the niceties of the twin religious guarantees in the First Amendment: free expression and no establishment of religion. Coupled with other organic concepts found in various documents such as the pursuit of happiness, religious toleration (from the Rhode Island colony, thereafter "adopted" as a general, if informal, principle), equal protection of the laws, the practices the very concept of democracy imposes, and so forth, the First Amendment guarantees clearly eschew any officially predominant religion, or its promotion, and further guarantees (to the extent fairness and civility can be enforced either officially or through mores and folkways derived from the nation's core principles) the ability of each belief system to seek its own rightful level, its place in the life of the nation, and the respect its system is entitled to.
To run such a complex system, your "public" ideology has to be one that promotes the values just listed. That can be done in one of two ways, but certainly not by trumpeting the triumph of Christianity, say, or one of its more aggressive sects. Aside from being inimical to our values, such a stance is absurd. The two ways are the ones I mentioned in the opening post here: universalism (admitting a deity, or not, but respecting each good faith effort to come to terrms with ultimate questions), or secularism (remove the concept of deity entirely from official promotion, but provide a milieu (much like universalism can) where such beliefs and devotions can flourish.
While as a strictly logical matter, it seems to me, the two approaches should be functionally and efficaciously equivalent, in practice, as the law has developed thus far, the nod seems to have been given to secularism as the official milieu on the theory that the simple promotion of religion at all, as Universalism does, even though equally, comes too close to "establishing religion," a prohibited activity and consequence.
