If this were so, new, and perhaps existing laws would be subject to religious restrictions and tenets.
But which ones?
Essentially, we would have a form of state religion. This opens an assortment of issues. First among them is, how many state religions? There are four basic possibilities. Zero state religion, which is what we have now, one state religion, which is the traditional implementation, several state religions, and all religions.
The really interesting one is having several state religions, and it is this one that I shall investigate. Some of the issues raised apply to other solutions as well.
The first issue is how to choose the religion. Historically, this was done by choosing the personal religion of the current ruler. So if you elect a Lutheran, everybody gets to be Lutheran for four years. The drawbacks here are obvious. People are not happy swapping their deeply held beliefs periodically; this rather undermines the whole idea of religion itself. Faced with penalties for disobeying, people would generally put on a façade of following the current belief system, and secretly continue to believe their own beliefs.
One way of minimizing this sort of stress is a grotesque parody of democracy, "choosing" a state religion by what the majority of the populace believes. An essentially similar approach is to simply vote on it. However, given the heterogenous nature of the United States, this will disenfranchise large sections of the population, likely even more than half.
However, there are ways to ameliorate this somewhat. Instead of choosing a specific religion (such as United Methodism), a more general category could be chosen (such as protestantism) or very general (such as Christianity).
But all of this smacks of hubris. Many religions posit a diety (or multiple dieties) with better knowledge than we posess. Therefore, the obvious approach is to write all the candidate religions (Santaria, Lutheranism, Pastafarianism, Deism, Pantheism, Agnosticism and so forth) on slips of paper, throw them in the air, and let God choose which religion to follow.
This could, naturally, go several ways. Suppose Shintoism were the one selected. Shintoism is a non-exclusive religion. As far as Shinto beliefs are concerned, a person could follow them as well as another belief system (such as Buddhism2). So it might seem that if a non-exclusive religion is chosen, we'd get to try again. However, it's not as simple as that. Suppose the second draw yielded Catholicism. While Shintoism technically allows Catholic beliefs, the reverse is not allowed. The Catholic belief system is closed, and does not permit other religious views (with some fairly specific exceptions).
Further, some religions, while not exclusive, are not compatible with each other. Followers of Ares cannot also follow Zoroaster in a coherent way. Others, even unexpected combinations, can at least theoretically coexist, as in The Force and Taoism. In fact, would could regard The Force and Pantheism as related in concept.
While many will object to the applied comparative religion involved, it will become necessary in order to have a thoughtful and inclusive solution to this problem. Some original thinking will be required to reconcile (say) Judeanism and Islam.
Also, a distinction must be drawn between religion and philosophy, and thought given as to how belief systems are composed of these and other facets, and which of these should inform legal decisions.
The situation becomes even more complicated given that our legal system is based upon the idea that laws are specific and definite, and that any reasonable person can make a repeatable, justifiable decision as to whether a law applies to any possible situation, and if so, how1.
Given this requirement for intellectual rigor, the chosen religion(s)' codes of belief and ethics must be distilled into implementable and definite rules.
Most of these beliefs spring from the religious writings of the various faiths. Some (such as Unitarian Universalism) are fairly broad in scope and offer little specific guidance. Others (such as Orthodox Judaism) comprise large amounts of specific laws, rules, guidance, and thousands of years of documented technical analysis of the implied, inferred, and extrapolated meanings.
How to apply this in legal venues requires even more decisions, each fraught with layers of complexity and repercussions. One obvious idea is to take a specified set of a chosen religion's writings /a litteratim/. But even this apparently straightforward approach has issues. Should the earliest known originals be used, in their original language? Or a synthesis of the best attested versions, culled from all available? Or a specific modern version or translation. Taking Christian writings as an example, should the book of Revelations be encoded into legal precedent? The Vulgate Bible? King James Version? Revised Standard Version? The Good News Bible? A mishmash of Greek, Hebrew, Aramaic, Latin, and English? Even if a decision is made to use the best current understanding of the extant materials, decisions remain as to who will implement these determinations, and whether the analysis well be repeated if new materials are discovered.
Another problem with literalism is that many of the laws in many of the possible religions are difficult to impossible to implement literally in today's society. Many religions contain a prohibition against killing. Would this outlaw war? Would our armies be legally enjoined to turn the other cheek? Or would all killing be outlawed? No more bug spray? Antibiotics? Lawnmowers?
Marriage is a hotbed of contradictory dicta3. Divorce could be impossible, trivial, or even required. Similarly with polygamy, incest, and many other very basic parts of the definition of "family".
1 Many current laws fail this test rather badly, it's an ideal to which we aspire, but not one we currently maintain.
2 Technically, Buddhism is more of a philosophy than a belief system.