Many conservatives think the Church has its proper sphere in society and politics has its own and though they may have many of the same goals their means to the same end must be different..
And any melding of the two corrupts both and imagine if the Church shared or surrendered, even by mistake, its moral capital to say...a Hillary Clinton? I prefer my religion to be above politics.
I don't know what having "In God We Trust" on our coinage has to do with "religious...imposition of dogma on (our) society", and I certainly don't understand how we got from that to the Patriot Act, but at least you've tacitly acknowledged that there are some extremely unattractive features of Anarchatarianism. BTW, are you implacably opposed to Federal imposition of martial law and states of emergency, because, like the Patriot Act, those are temporary measures designed to protect us in times of deathly peril, though I suppose that some might refer to them as "sacrificing liberty to gain security". I think of them as proving that the Constitution is not a suicide pact.