On tv shows like “Cheaters”, why are some people’s faces blurred out and others’ aren’t? How do they decide?

The spouses are shown but the third party is usually blurred, especially if they refuse to sign a release.

As said, it has to do with consent.   If people don't consent to having their faces seen, they are blurred out.

People who don't sign waivers to appear are blurred out.

They refused to sign the papers participating in the show. Blurs don't get paid.

The ones that won't sign a release form allowing their faces to be shown are blurred out.

Most of the filming is faked situations, based on real occurrences. [read the fine print at the end of the broadcast.]

Some ARE REAL, if the participant does not sign a Release, the face has to be blurred.

Likely based on the desires of the people whose faces are blurred.  If you use someone's likeness in your movie or TV show without their permission, you're in lawsuit city unless it's news or 'fair use'.  So IF the show is actually filming incognito (very unlikely...you're probably watching alot of staged stuff mixed in with some real stuff), they would approach the people after and ask for permission in exchange for money.  If they say no, they get blurred.

I surmise that people without blurred faces signed a release (and were probably paid) to allow showing their face.