The critical definition of conservatism, by which I mean that political tradition Burke founded, rests on a distinction between theoretical and practical wisdom. Burke insisted that abstract ideas of the Truth should not be our guide in political thought and action. He foresaw what would happen when tradition ceded to absolutism in the French Revolution. He prized experience, the wisdom of time, and the adaptation of existing institutions to new social realities. So for conservatives, the core political virtue is practical reason and common sense, not ideology, theology or absolutism.
Now check out the latest Pew poll question:
When it comes to questions of right and wrong, which of the following do you look to most for guidance?
Most Americans have a healthy respect for religious teaching but in their lives give greater preference to common sense and practical experience. That includes almost all religious groups as well - Catholics, in particular, show conservative tendencies. The exceptions? Evangelicals and Mormons and Jehovah's Witnesses - who are trained to forego practical reasoning for abstract truths based on unquestionable authority. Evangelical Christians are much less conservative than American Muslims, for example.
The Republican party is not, at this point in time, a conservative party, as Burke would understand it. It's a fundamentalist religious party. Until the influence of evangelicals and Mormons is reduced, it will find these tendencies reinforce each other.