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The 16-year-old's mom is former White House counselor Kellyanne Conway, and her dad is anti-Trump lawyer George Conway.
Claudia went viral last year for exposing political differences within her family's Alpine home.
During her "American Idol" audition, the teen admit music has been there for her during dark times incited in part by negativity online.
"When life is going downhill, I have my music," she told the judges. "I'm a singer, and this is what I want to do."
Claudia began with a rendition of "Love on the Brain" by Rihanna, but switched to "When We Were Young" by Adele, after her nerves got the best of her.
While Luke Bryan gave Claudia a hard "no," fellow judges Katy Perry said "I can get behind ya." Lionel Richie said: "You chose music, I'm going to give you a shot at music."
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