I invite you to join in propagating a new meme: "neo-theo".
Despite its obvious resonance with "neo-con", the term "neo-theo" more closely parallels the rebranding that the creationist movement undertook after getting repeatedly slapped down for making its religious motivations too visible. They went back into their burrows and emerged again as defenders of "academic freedom" (religious zealots have a free-speech right to indoctrinate school children about "evilution") and "intelligent design" (a pseudo-scientific label for the laffably named Discovery Institute, which operates no labs, runs no experiments, publishes no papers, and has never discovered a damn thing). The legal, academic, and scientific false fronts they put up are mere sham, of course, but they help to preserve the legal facade of not being religiously motivated.
It's the same deal with the neo-theos. Instead of being repackaged creationists, they're gussied-up dominionists. In their heart of hearts, they believe the United States should be (and probably all along was intended to be) a theocracy, but they've learned from bitter experience that they can't come right out and honestly say so. Instead, they take refuge behind nominally secular legal concepts, such as the idea that corporations are people (which gained legal credibility after the eye-opening Supreme Court decision in Citizens United v. FEC) and thus entitled to "human rights", such as conscientious objection.
There's another case currently headed for the US Supreme Court, in which the newly minted "person" known as Hobby Lobby claims its conscience has been shocked by being required to provide the same kind of health-care coverage for its employees as, say, General Motors or Microsoft. In fact, while the fundamentalist owners of Hobby Lobby may have just such an attitude (the same way that the owners of Chick-fil-A are opposed to gay marriage), the corporation itself, not being a human being, is devoid of opinions on the subject. And the law applies to the corporation.
Just as with the "academic freedom" claims of the creationists, the neo-theos are attempting to put a smiling secular face on their ludicrous claim, wrapping it in shiny colored paper with a ribbon, a bow, and a label reading "religious liberty". Well, "corporate personhood" (either as such or in its guise as "church personhood") is as much an oxymoron as "intelligent design" and deserves to be exposed for what it truly is: dominionist dogma rebranded for secular consumption.
I believe that identifying its proponents as "neo-theos" (which has the added advantage of rhyming) will help to do that.