These folk aren't trying to eat less, though. They're just eating and writing it down. If it were a diet project, you know I'd be way more obnoxious about it.

I think the function of privilege awareness is as a check on asshattery. If I were, for instance, to assume that everyone else could and should eat like I eat (as I sometimes do), I'd be a privileged jerk for not recognising that not everyone has access to my posh diet. There's a difference between worrying about privilege and just noting it; it's like conceding one's own bias.