Appearing Sunday on CNN, Democratic presidential hopeful Pete Buttigieg disagreed with Beto O'Rourke's proposal to tax churches opposed to same-sex marriage.

On Thursday, nine presidential candidates discussed LGBT issues during an HRC-sponsored town hall broadcast on CNN during prime time.

(Related: Nine Democratic presidential candidates discuss LGBT issues on prime time.)

During the event, moderator Don Lemon asked O'Rourke, a former congressman from Texas, whether “religious institutions … should lose their tax-exempt status if they oppose same-sex marriage.”

“Yes,” O'Rourke answered. “There can be no reward, no benefit, no tax break for anyone or any institution, any organization in America that denies the full human rights and the full civil rights of every single one of us. And so as president, we’re going to make that a priority and we are going to stop those who are infringing upon the human rights of our fellow Americans.”

Buttigieg told State of the Union host Jake Tapper that he disagreed with O'Rourke.

“I agree that anti-discrimination law ought to be applied to all institutions, but the idea that you're going to strip churches of their tax-exempt status if they haven't found their way toward blessing same-sex marriage – I'm not sure he understood the implications of what he was saying,” Buttigieg said.

“That means going to war not only with churches, but I would think, with mosques and a lot of organizations that may not have the same view of various religious principles that I do, but also, because of separation of church and state, are acknowledged as non-profits in this country.”

“So if we want to talk about anti-discrimination law for a school or an organization, absolutely they should not be able to discriminate,” Buttigieg said. “But going after the tax exemption of churches, Islamic centers or religious facilities in this country, I think that’s just going to deepen the divisions that we’re already experiencing.”

Buttigieg is the nation's first openly gay and married presidential candidate.

(Related: Pete Buttigieg: America is ready for a gay president.)