There is a split developing between the Paulian and the theocrat wings, and their fundamental objectives are indeed in conflict, but don’t get your hopes up too much that their alliance of convenience will collapse in ruins any time soon.

They share many basic positions, most especially opposition to federal involvement in education, civil rights, healthcare, environmental regulation etc. Some of the more perceptive Dominionists realize that they cannot achieve a true theocracy in one step and they consequently see the Paulian agenda as an intermediate step that would essentially clear the boards for them and greatly simplify their accession to power.