They argue Samaritan's Purse and the Billy Graham Evangelistic Association, nonprofits he heads, "are complicit" in spreading misinformation about the election.
The announcement comes as Franklin Graham is slated to speak at the Republican National Convention this week.
Evangelical leaders would "take the shameless conman [Trump] over the principles that they're preaching in the holy season as we celebrate Jesus," Sharpton said.
Franklin Graham said that his father, Billy, who founded the magazine would be "very disappointed" in the editorial.
Manuel Torres claims being alone in a patrol car with a female trainee would give "the appearance of sinful conduct," invoking the so-called "Mike Pence rule."
Outrage over politicians obeying the rule notably cropped up in 2017, when The Washington Post reported that Vice President Mike Pence does not dine alone with a woman who is not his wife.
Billy Graham's 16-week New York Crusade attracted thousands of people and cemented the reverend's place in history.
A 2007 biography of Billy Graham explores his love for people and leadership.
America's best-known Christian evangelist died has died at 99. Jon Meacham profiled profiled him in 2006.
Graham wrote more than 30 books and founded the Billy Graham Evangelistic Association in 1950.
He has lined up six clerics —one more than the previous record-holder Nixon
The campaign and local officials had said they expected more than 30,000 people, but far fewer arrived.