Noam Scheiber thinks not:
The reason conservatives have traditionally done better in presidential elections is that they have the luxury of running to the center. Consider, for example, George W. Bush. Precisely because no one doubted his conservative credentials—the man’s favorite philosopher was Jesus Christ, for God’s sake!—Bush could style himself a minority-loving, compassion-exuding moderate without worrying that conservative mau-mau-ers might pounce at any moment. Recall that it was Bush who, back in October of 1999, criticized House Republicans for trying to “balance their budget on the backs of the poor.”
I agree with Noam's broad point. But this also reveals just how corrupted religion has become in America. Since when does professing that your favorite philosopher is Jesus Christ mean you are a Republican, let alone a conservative Republican? Since the emergence of the Christianist right.