But Monica Cole, director of One Million Moms, said the show is "blasphemous, irreverent and disrespectful." Her group is basing its criticisms on the show's YouTube trailer, which shows Jesus using explicit language and includes violence and drinking.
She, like other critics, hasn't seen a full episode yet.
One Million Moms does not typically go after shows intended for adult audiences, but Cole said, as a "Christian ministry, we felt like we could not excuse this behavior for any television company."
It's "extremely sad when mocking someone's faith is someone's entertainment," she said.
"Black Jesus" will air late at night, well after most kids are in bed, but Cole said the time of day is almost irrelevant. "No excuse, blasphemy is blasphemy, no matter what time of day it is."
In a statement, Adult Swim said "Black Jesus is a satire and one interpretation of the message of Jesus played out in modern-day morality tales; and despite what some may consider a controversial depiction of Jesus, it is not the intent to offend any race or people of faith."
One Million Moms and the American Family Association, which have previously targeted Honey Maid graham crackers,the Disney Channel show "Good Luck Charlie" and J.C. Penney for gay-friendly messages, have launched a campaign asking people to send an email to the Turner Broadcasting to pull the show before it airs. Supporters have sent more than 131,000 emails, according to the AFA.
A similar petition to cancel the show, started by a group called Christian Network, has reached almost 7,000 signatures.
If the show stays on the air, Cole said, her group would go after the show's advertisers. For now, an Adult Swim representative said Turner has no intentions to cancel "Black Jesus."
DeWayne Wickham, dean of Morgan State University's School of Global Journalism and Communication, wrote in USA Today that the show should stay on the air because it may actually convert people.
Referring to McGruder, Wickham wrote that "there's always a positive message buried just beneath the outrage that he doles out."
Wickham argued that Jesus' original disciples came from questionable backgrounds, just like in the show, and "though a pastor might tell these stories in church, such a message of deliverance from a life of sin might not reach deep into McGruder's audience," Wickham said.
This is not the first time racial depictions of Jesus have raised eyebrows. Last December, Fox News anchor Megyn Kelly irked black audiences when she said, "Jesus was a white man, too. It's like we have, he's a historical figure that's a verifiable fact, as is Santa, I just want kids to know that."
Robert Thompson, director of the Bleier Center for Television & Popular Culture at Syracuse University, said Jesus has been a tricky subject for artists going all the way back to Michelangelo's frescoes in the Sistine Chapel.
"There has been a lot of visualizations of Jesus that have been on a whole spectrum of what might have been considered an accurate depiction of what he might have actually looked like," Thompson said.
But Thompson said he believes a lot of people who are upset about the show might be more concerned with "contemporary culture wars" rather than the show's actual message.
"By and large, if you go to the actual basic teaching of love and turning the other cheek and feeding the poor, they are very, very good messages," Thompson said. "And to me, if you can get to the base of that kind of story, it can be told in a lot of different contexts."