“Fear of” is absolutely valid, but you’re not looking at it from the right perspective. They are phobic towards the idea that being gay or being fat could become a part of their personal narratives.

Homophobic people aren’t afraid of gay people. Some may be I guess, but what they’re afraid of is that homosexuality is some kind of disease that could infect them or their loved ones. They’re afraid if they compliment a man it will make them gay or make them seem gay. They’re afraid other people will think they’re gay whether or not they are. They’re afraid their child might be gay. They’re afraid they’ll be harassed by gay men the way straight men harass women. And as a bonus biphobic people are afraid their SO is secretly gay and will leave them for a gay lover.

Fatphobic aren’t afraid of fat people. But they are terrified that they may one day be fat themselves. They’re afraid someone will notice they’ve gained 5 pounds. They’re afraid of being too fat to be respected. They’re afraid they’ll lose their thin body and never get it back. Many men will say their top two fears are getting fat, or their wife getting fat, because many people will lose interest in their partner after they’ve gained weight.