Democratic presidential hopeful Pete Buttigieg on Sunday said he wasn’t sure that 2020 rival Beto O’Rourke understood the implications of Mr. O’Rourke’s call last week for groups that oppose same-sex marriage to lose their tax-exempt status.

“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,” Mr. Buttigieg, mayor of South Bend, Indiana, said on CNN’s “State of the Union.”

“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 acknowledged as non-profits in this country,” he said.

At a town hall devoted to LGBTQ issues last week, Mr. O’Rourke, a former congressman from Texas, said groups that oppose same-sex marriage should have their tax-exempt status revoked — a stance that drew swift pushback.

Mr. Buttigieg, who is openly gay, said institutions like schools should not be allowed to discriminate.

“But 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.

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