That dissonance is something that Mr. Trump’s rivals are trying to bring to the attention of religious voters. Last week, former Gov. Jeb Bush of Florida released a video that highlighted Mr. Trump’s previous liberal ideas and New York sensibility.

“I lived in New York City and Manhattan all my life, O.K., so my views are a little bit different than if I lived in Iowa,” Mr. Trump is shown saying in an old television interview, explaining why his views were different from those of many Republicans.

And Ben Carson, the retired pediatric neurosurgeon who is running second to Mr. Trump in some recent polls, said Wednesday that while his faith is “a very big part of who I am,” he doubts that is true for Mr. Trump. “I don’t get that impression with him,” he said.

Few recent episodes have illustrated how differently Mr. Trump sees the world than his comments on Planned Parenthood, some social conservative leaders complain. On the question of whether to strip the organization of its $500 million in federal funding, he has said that he would but that he also believes it should be evaluated as more than just an abortion provider. The issue will be debated in Congress in the coming weeks.

“I would look at the good aspects of it,” he told CNN. “And I would also look because I’m sure they do some things properly and good, good for women, and I would look at that.”

Few Republicans today would dare utter anything complimentary about Planned Parenthood, which is such a contentious subject that several candidates for president have said they would like to see the effort within Congress to eliminate the organization’s funding escalate into a government shutdown if necessary.