My memory might be faulty, but it seems like religious influence on politics got obvious in the eighties with the so-called Moral Majority. I can understand how some religious perspectives can intersect with politics. Whatever you think about the anti-abortion crowd, a lot of them, right or wrong, sincerely believe that aborting a fetus is killing a human being and should therefore be illegal. If you truly believe this, then it makes sense to push for anti-abortion laws. I disagree with their position and see their premise that a fetus is a human being, not a potential human being, as being religiously based, and therefore a poor foundation upon which to base laws that apply to all, but I see their point. But what we have seen in the last twenty years or so is using religion as an excuse to impose laws that are based on individual or group prejudices and biases.
The law states that it is illegal to discriminate based up several criteria such as race, national origin, religion or gender. Yet there has been a push, which is supported by "conservative" judges, to exempt religious groups from these laws and even to exempt individuals who claim religious objections to a wide range of laws. It used to be that a law had to impose an undue burden on religious expression for an exemption based on religious belief to be granted, but we are moving to a place where anyone can, without any basis, claim a religious objection to any law simply because they don't like it. Or just don't want to comply. Religion is being elevated to a position of primacy in our society. Or at least the dominant religion is.
Even among adherents of the dominant religion, objections need not be based on anything actually found in a religion's holy book, creed, dogma or officially sanctioned pronouncements, but can simply be stated as "this is against my religion". We are seeing this most obviously in the widespread objection to vaccination requirements and mask mandates, often based upon the claim that they are taking away "our freedoms" (note the weird plural) when these people would be hard-pressed to find any documentation in their religion's sacred texts about unlimited freedom(s). If anything, it's the civic religion of "owning the libs".
Unfortunately, due to an irrational dislike of Secretary Clinton and an over-the-top concern about emails we enabled Mitch McConnell to sew up his lifelong agenda to remake the federal judiciary. We now have a Supreme Court majority that views with sympathy these calls for religious nationalism, dominionism, and elevating spurious religious claims above the secular.