Cruz has been among the more outspoken Republican presidential hopefuls opposed to same-sex marriage, but when pressed by Page, he cast the argument as one about religious liberty.
“What about the question about LGBT people being fired for just strictly being gay or trans?” asked Page, who was wearing a cap and sunglasses.
“Well, what we’re seeing right now is actually, we’re seeing Bible-believing Christians being persecuted,” Cruz said.
“Yeah, for discriminating against LGBT people,” Page interrupted him. “No, for living according to their faith,” the GOP presidential hopeful fired back.
“Well, then people would have used that argument in the segregation era,” Page insisted.
“No one has the right to force someone else to abandon their faith and their conscience,” Cruz later told Page, as reporters and other fairgoers gathered around during the five-minute encounter.
Page was at the fair to shoot her new Vice show, called “Gaycation,” where she travels the world to explore local attitudes about LGBT culture.
Cruz went on to claim that the Obama administration and the left have paid little attention to the execution of gays in ISIS-controlled territory in Iraq, Syria and Iran.
ABC News asked Cruz afterward whether he knew to whom he had been speaking, and he said he didn’t.
Page came out as a lesbian in a speech before the Human Rights Campaign in 2014.
Page was interviewed for Variety‘s recent marriage equality issue following the Supreme Court’s ruling in favor of same-sex marriage. She is set to star in the lesbian drama “Freeheld,” about a real-life same-sex couple’s legal battle to get pension benefits after one of them (Julianne Moore) is diagnosed with cancer.
ABC News captured the exchange: