They are edible in the strictest sense of the word, but IMHO they are parts of the animal that should have been tossed into the garbage. Seeing this stuff in my bowl of soup is equivalent to seeing little pieces of garbage floating around in it.
For example, when I make chicken soup, I use thighs to get the heartiest broth. I tear the meat up by hand, carefully combing through it to pick out any bones, gristle & fatty pieces. There is nothing worse than enjoying a bowl of homemade chicken soup and discovering a surprise piece of chewy gristle in your mouth. God help me if I happen to be in public when this happens because the offending matter & whatever else happens to be in my mouth gets spat out into a napkin or the nearest trash can.
But I run into this all the time. When I get fed other people’s homemade soups, and can see pieces of fatty skin or gristly tendons floating in the bowl I have to eat as though I’m picking through a mine field. Careful not to touch the “inedible” things. My Asian friends seem to be the worst offenders, even tossing entire bones into the pot, and then dish everything right into your bowl.
I know the fat & bones add flavor, but tie them up in cheescloth, or strain them out of the stock pot for god sakes. Don’t make me look at that nasty stuff when I’m trying to enjoy the dish!
Gristle is especially nasty - it’s like chewing on rubber bands. You just chew and chew and chew and chew… Do you just swallow the grislte? Do you even try to chew it up?