LOS ANGELES, Calif. --

Her opinions on same-sex marriage may have cost Miss California the Miss USA crown on Sunday night – but in an interview with Billy Bush for “The Billy Bush Show” and Access Hollywood on Monday morning, Carrie Prejean revealed that her sister is a gay rights activist.

“My sister is a second lieutenant in the Air Force and she is a gay rights activist,” Carrie told Billy.

Her sister, she added, is not gay.

“No. She supports gay people, she supports gay marriage. My beliefs have nothing to do with my sister or my mom, or whatever.”

Nor was her sister offended by her comments on Sunday night.

“She was just in my hotel room and she said, ‘Sis, I’m not offended by anything that you said. We have two different opinions and I love you because of it. I love you because you stood up for what was right, and it’s not a matter of being gay or not gay, it’s a matter of you competing for Miss USA and getting a question and answering it to the best of your ability.”

At the Las Vegas pageant, Carrie took a question on same-sex marriage from judge Perez Hilton, who asked her how she felt on the subject.

“In my country, and in my family, I believe that a marriage should be between a man and a woman,” she said on Sunday night. She went on to come in second to Miss North Carolina.

“It did cost me my crown,” Carrie told Billy, who co-hosted the ceremony, on Monday. “I wouldn’t have had it any other way. I said what I feel. I stated an opinion that was true to myself and that’s all I can do.”

“It is a very touchy subject and he is a homosexual and I see where he was coming from and I see the audience would’ve wanted me to be more politically correct,” she added. “But I was raised in a way that you can never compromise your beliefs and your opinions for anything.”

But her sister has different beliefs.

“She has her own views,” Carrie said. “She’s a 22-year-old woman who’s in the Air Force who’s extremely educated. She debates with my dad all the time about it. That’s what’s so great about being an American – we’re able to have our own opinions.”

And Carrie said she’s had plenty of support for her performance since the pageant.

“I feel like I won. I feel like I’m the winner. I really do, Billy,” noting that on Monday, she had 1,000 messages on Facebook and 2,000 friend requests.

As for Carrie’s own love life, she wants to keep it private.

“He is a great man,” she said on rumors of dating Michael Phelps, laughing in response to Billy’s questions. “Wouldn’t you like to know, Billy Bush? We can talk about that a different day.”

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