If former “American Idol” contestant River Gibson played Cajun music, he could be gigging in his native Acadiana every day. But waltzes and two-steps never moved him. Green Day did.

“I appreciate Cajun music,” said the 24-year-old singer-guitarist in the modern rock-pop trio LVVRS. “But it never called out to me. Growing up, bands like Green Day and Foo Fighters and Coldplay inspir...