Folau was sacked by Rugby Australia in May for a "high-level breach" of contract after the full-back posted "hell awaits drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolaters" on Instagram.
Cheika overlooked Folau before he was sanctioned, stating "the team is king", and the Wallabies boss has revealed that stance did not go down well with some supporters.
"People were saying all sorts of stuff," Cheika said. "Just threats I was getting; people on the street, some to my face, a couple at some games. It was just crazy stuff."
Cheika is disappointed not to have Folau in his Rugby World Cup squad, but has no issue with the 30-year-old expressing his opinion.
"I'm not disappointed in the individual because if that's what he believes, and that's where his passion is, I will never tell someone to hide it," he added.
"I might not agree with everyone, but I'd never want someone to not say what they feel. I'm no person to judge.
"The other disappointing part is that we lost one of our best players; a guy who I helped come back.
"I wouldn't say I'm responsible for what's happened. It's just life. But I had to do what was needed for the team."
Australia opens its Rugby World Cup campaign next Saturday when it takes on Fiji in Sapporo.