CHARLOTTE, N.C. — One, the president of the Christian university his father founded, raised eyebrows and provoked an outcry among some evangelicals when he endorsed Donald J. Trump before the Iowa caucuses.

Another, a son of perhaps the nation’s most celebrated evangelist and the successor to his father’s ministry, has drawn attention for his scathing comments about Muslims and is in the midst of what he describes as a 50-state tour “to challenge Christians to live out their faith at home, in public and at the ballot box.”

Jerry Falwell Jr., whose father, the Rev. Jerry Falwell, founded Liberty University and the Moral Majority movement, and the Rev. Franklin Graham, whose father, Billy Graham, is estimated to have preached the Gospel to millions of people, now find themselves forces of their own. Both are trying to balance their own identities, and their father’s legacies, at a time when religion is playing a powerful role in American politics.

The excitement among Christian voters has been on display this month in Iowa, which held caucuses Feb. 1, and South Carolina, where Republicans will vote on Saturday and Democrats on Feb. 27. Similar dynamics could prove pivotal as conservative candidates also seek support in the nine other Southern states where Republicans will vote by March 5. The stakes are high for Mr. Falwell, who is not a pastor, and Mr. Graham as they ponder the rewards and perils of creating political identities apart from the ones their fathers forged decades ago.