Well, one segment of the conservative/Republican movement is Neo-conservatives. Who are not religious-right.

The original neocons were anti-Stalinist Marxists. They moved farther and farther right. Religiously, they were likely to be Jewish, mainstream Protestant, or not-fervent Catholic. They approved of religion because it was a defense against Communism.

Another segment are economic conservatives.

Both groups tend to get annoyed at Christian Conservatives because they insist on injecting religion where it doesn't belong -- wasting money on charity, for example.