Democratic presidential candidate Beto O'Rourke doubled down on his proposal to revoke the tax-exempt status of religious institutions that do not support same-sex marriage.

The former Texas congressman reiterated his support for punitive tax measures against churches or affiliated services that believe marriage is between a man and a woman, a position he introduced at CNN's Equality Town Hall on Thursday evening. NBC host Geoff Bennett asked O'Rourke how he would implement this plan given that the government "can't just dole out punishments on theological grounds."

"You are free to believe anything that you want to in this country, to associate with whom you please, to practice your faith as you best see fit, but you are not allowed to discriminate against people in this country," O'Rourke said during a Sunday appearance. "What I'm talking about is making sure that we follow the letter and the spirit of the law, and that as president I will sign into law the Equality Act to make sure that we do not deny the civil rights and human rights of any of our fellow Americans based on their sexual orientation or gender identity."

House Democrats passed the Equality Act in May. Critics say that it will not just protect LGBT people, but punish those with traditional religious beliefs. The legislation could undermine Religious Freedom Restoration Acts at the state and federal level and would strike down "religious freedom protections for private citizens if they exercised their consciences in running their own businesses."

O'Rourke went on to say he believes any nonprofit organization that is going to deny equal treatment under the law to Americans in the "LGBTQ community" will be held accountable, saying he would withdraw their tax-exempt status.

Bennett pressed O'Rourke on the unintended consequences of this policy, noting that it could also be used to target "conservative black churches, mosques, Islamic organizations, orthodox Jewish communities, [and] a number of religiously affiliated HBCUs."

O'Rourke responded that a religious organization simply professing opposition to same-sex marriage would not be enough to void its tax-exempt status. Rather, religiously affiliated service providers—those in "higher education, or health care, or adoption services" for example—that "discriminate or deny equal treatment under the law based on someone's skin color or ethnicity or gender or sexual orientation" would be at risk.

"If one of these nonprofit institutions persisted in that kind of discriminant treatment of our fellow Americans, we would look at revoking their tax-exempt status," he said.

Democratic presidential candidate Pete Buttigieg, who is married to a man, criticized O'Rourke's proposal on Sunday, saying that O'Rourke does not understand its implications. During an appearance on CNN's State of the Union, he raised the same concerns Bennett had.

"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 the separation of church and state, are recognized as non-profits in this country," Buttigieg said.

Buttigieg said that he supported anti-discrimination rules "for a school or an organization," but that targeting the tax-exempt status of religious institutions themselves would be destructive.

"Going after the tax exemption of churches, Islamic centers, or other religious facilities in this country, I think that's just going to deepen the divisions that we're already experiencing," he said.