The ACLU uses the courts to override the will of the people. It also has the media in its pocket.
One route to wider public acceptance for an intrusive role of religion in government is to obtain control of public schools. The American people, right now, would not accept the stoning of disobedient children or the execution of homosexuals and apostates. But they did once, and there's no reason to believe that their attitudes, having been changed once, could not be changed again.
But these people are nowhere close to obtaining control of public schools. And furthermore, history shows that religious (or other) extremism doesn't take hold of a country in normal times, but rather in abnormal, crisis-ridden times. And if we should be faced with a crisis of the type that historically has given rise to it, then it'll happen whether it's sanctified by the establishment or not (in fact not being sanctified can accelerate it, as in the case of the American Puritanism that you referred to in your post). It's far too distant and theoretical a concern for it to be taken seriously as a matter of public policy, especially when the trend is so manifestly in the opposite direction.
And it's also comparatively easy to use public schools and popular media to entice people, and especially children, to socialism, multiculturalism, and other "feel-good" stuff. A lot harder to entice them to Draconian religious impositions. Accomplishing that requires a whole different set of prerequisites that just don't exist in the U.S. today.
That's your opinion. I would have agreed with you five years ago; but having seen fundamentalists impose a religious agenda on the teaching of biology in Ohio, Kansas, Dover, and elsewhere, I no longer agree. I would have thought it impossible that they would try to overthrow much of modern science and attempt to substitute biblical literalism for it. Yet they did. I'm not waiting for the next action item.
As a scientist, this is a hot button issue for me, as, say, abortion is for others. And many scientists, maybe even most, feel the same way. If the GOP or a GOP candidate endorses creationism, it forfeits my support (though given its love of federal spending, illegal immigration, affirmative action, etc., I'm not sure why any conservative continues to support the GOP anyway).