I'd rather he didn't. I don't want him or us having to dramatically alter his our presentations to single out a specific group. His and our message overall appeals to everyone that is willing to open their ears and listen. Changing tones so dramatically can alienate others and even come back to bite us in the butt later on.
First, I think the OP was talking about US, not the official campaign. We, as door-knockers and phone callers, need to relate to who we're talking to.
Second, there's a difference between "going off the deep end" and being consciously empathetic to a particular audience. No one is calling for you or RP to talk about the end times, purging the world of sin, etc. - instead it should be recognized that the typical IA, NH, and SC GOP primary voters are likely to place a high value on a candidate who believes in Christ as their personal savior, and lives accordingly.
So, it's the little things that need to happen: end your phone calls with "Have a bless
ed day!", imply that you're doing "good works" by proselytizing door to door, or if you get into a policy discussion try to analogize to the teachings of Jesus.
These are things that you can do, even if your not Christian, without being disingenuous. And none of these little things will be able to be used against the campaign in the general election when the audience changes. It's not about a dramatic change in tone, it's merely about focusing the message to the audience.