You can describe anything in a way that makes it sound unfunny. Having a quick temper is also a comedy staple, but that's also tied to mental health conditions....
False equivalence - there's a big fuckin' difference between laughing at a comedy character and laughing at and making fun of real people to their face, or even behind their back for that matter. Even if the comedy character is acted by an actual fat guy and the joke is that he's fat it's still two different things. For one thing the actor in question, say Kevin James for a lazy example, has decided to use his physical appearance as the basis of his career. He's intentionally and willingly put himself out there specifically for people to laugh at him in return for cash. That fat person you knew at school? That fat guy at work? They haven't done that. They have not consentually offered themselves to you for your amusement. And as for characters like Homer Simpson or Peter Griffin? Well they don't even exist. For a non body related example of what I mean, using Homer, I'm sure you've laughed at Homer strangling Bart at some point in your life, but would you laugh at a real father strangling his real child? I bloody well hope not. I hope you'd call the police.
Have I laughed at the antics and misfortunes of fat/skinny/angry characters in fictional shows and movies? Yes I probably have. But IMO there is nothing funny in real life about fat/skinny/angry people (I mean have you ever known someone with a seriously bad temper? They ain't funny, they're fucking terrifying and upsetting) and if you mock and laugh at fat/skinny/angry people in real life then you're an asshole and you can go fuckyourself.
As for fundies - yeah but not all fundies are fundies due to health problems (in fact in my experience most are not mentally ill, I'm from Northern Ireland we got a lot of 'em so I know plenty and none of them are fundies due to mental illness) and the ones that aren't mentally ill are fair game because fundamentalism is basically just an opinion, and opinions are fair game if you're sound of mind. Opinions are a direct reflection of who you are as a person and if you're a fundie you're likely bad person on some level. Like being a Nazi - it's an ideology, an opinion...and it makes you a bad person. Being fat is ALWAYS linked to health problems....being fat IS a health problem, there are no exceptions. And being fat is not an opinion you hold, it does not automatically demonstrate you are a horrible person. You can be fat and be a terrible human being, but the two aren't connected. Plus as far as I know obesity doesn't cause people to deny gay people the same rights as everyone else and tell them they're going to hell or blow up abortion clinics. Some people who've done such thigns may be fat but it's coincidental, they didn't do it because they're fat.
We have actually had obviously mentally ill fundies being mocked on FSTDT in the past, on at least one occasion that I remember, and I did actually say to everyone basically, "This guy is clearly an actual schizophrenic. I'm not ok with making fun of the mentally ill we should be better than this. Can we cut it out please?" and people did stop it. So when we do come across one who is actually mentally unwell, and someone points it out, we drop it. Coz to paraphrase George Clooney from Dusk 'till Dawn, we may be bastards but we're not fucking bastards.