"We're hypocrites if we don't make it for that reason," Parker told the Television Critics Association's summer meeting this week.
The 63-year-old soul singer had voiced the Chef character on "South Park" since 1997, but quit earlier this year because of what he said was the animated show's religious "intolerance and bigotry."
"It was so crazy because we got along so well. And that's where we were like, `Wow, you really thought the show was fine until we did your religion, and now we're bigots,"' Parker said.
Stone said Hayes asked them to have Comedy Central pull the episode before it aired last November and not make it into a DVD. They refused.
"Trapped in the Closet," which skewers Scientology and its popular proponent Tom Cruise, was set to repeat in March but was pulled off the air by the network amid published reports that Cruise had used his clout to bury it.
"We just picked the wrong guy to parody because I have a feeling we'll be asked about Tom Cruise for the next two years," Stone said. "Every time we're in a headline, it's like, Tom Cruise and then us in a headline, you start to get that Tom Cruise stink on you."
"Trapped in the Closet" will hit the airwaves again July 19.
A spokesman for Comedy Central has said the network rotates its 150 episodes of "South Park" in and out of the broadcast schedule.