Wearing a hat and sunglasses, Page approached Cruz in a video caught by ABC News and asked him about "LGBT people being fired for being gay-trans."
"Well, what we're seeing right now, we're seeing Bible-believing Christians being persecuted for living according to their faith," Cruz said.
"People would have used that argument in the segregation era," Page responded.
"Now I'm happy to answer your question, but not to have a back-and-forth debate," said Cruz, before continuing. "No one has the right to force someone else to abandon their faith and their conscience," he said. "Imagine, hypothetically, you had a gay florist and imagine two evangelicals wanted to get married and they decide, 'You know what, I disagree with your faith and I don't want to provide flowers.'"
Cruz and Page spoke for more than five minutes, but the senator never caught on to the actress' identity. According to her publicist, Page was in Iowa working on a project for Vice.
Check out her full conversation with Cruz below.