DES MOINES — Sen. Ted Cruz and actress Ellen Page had an animated back-and-forth about gay rights at the Iowa State Fair on Friday.

Page asked Cruz, who was standing behind a grill full of pork chops, about LGBT people who are "being fired for just strictly being gay or trans." The question kicked off a nearly five-minute exchange between the actress and the presidential candidate, who did not appear to recognize Page.

"We're seeing Bible-believing Christians being persecuted for living according to their faith," Cruz said. The Texas Republican, who is courting the vote of conservatives and evangelical Christians, is holding a rally for religious liberty here Friday night.

"For discriminating against LGBT people," Page shot back. The encounter was filmed by ABC News.

"No, for living according to their faith," Cruz, holding a pork chop in one hand, responded.

Cruz said he would answer Page's question but "not have a back and forth debate," which is exactly what they ended up doing. The two launched into a debate about gay rights and religious liberty. Page said Cruz's arguments about religious liberty were similar to those used during segregation. Cruz recounted the story of an Iowa couple who refused to hold a same-sex wedding at their venue.

"Imagine, hypothetically, that you had a gay florist and two evangelical Christians wanted to get married, and the gay florist decided, 'You know what? I disagree with your faith and I don't want to provide flowers,' " Cruz said.

"I would say they should provide the flowers," Page, who has appeared in movies including "Juno," said. Page is a lesbian.

Page said to Cruz that "gay people used to be thrown in jail" and that "we've come a long way."

"Do you know where gay people are being persecuted right now?" Cruz asked?

"All over the world," Page said.

Cruz said that gay people are being killed by the Islamic State and in Iran.

"And on the left you hear complete silence about Iran hanging homosexuals," Cruz said, adding that the Obama administration is sending "millions of dollars" to the country.

"That's not true!" Page exclaimed while he was speaking. Page said that gay people are being persecuted around the world, including in Jamaica.

"Does it trouble you at all that you draw a moral equivalence between Christians in Jamaica and radical Islamic terrorists in ISIS who are beheading children?" Cruz said, using an acronym for the Islamic State.

Jamaica "may not be celebrating a gay pride parade, but they're not murdering people," as in Iran or the Islamic State, Cruz said, and asked why the Obama administration isn't raising the issue.

"I would love to talk to Obama about it. That'd be great," Page said.

"Well, good, then we're agreed on it," Cruz said.

"No, no, we're not. Don't do that," Page said.

"Ma'am, we've had a long discussion," Cruz said.

"Yeah, yeah, I appreciate it," Page said.