I think the best way to fight knee-jerk reactions to pop culture discussions, to resist the sense that one is being personally attacked, is to step outside the equation, and to step away from the keyboard to do some thinking. Remember that the writer probably doesn't know you, isn't thinking about you while writing the piece, and doesn't think that you are a bad person. The writer is just discussing something seen, an embedded message.
After all, you didn't create the piece of pop culture under discussion. You may be complicit in the social attitudes that it embodies, but that often happens on an unconscious level. You are not responsible for not seeing everything in all things, but you are responsible for seriously evaluating and considering critiques pointing out things you didn't see.
The fat acceptance movement has been active for a long time. The National Association to Advance Fat Acceptance has been around since 1969, challenging social attitudes about fat and fighting for fat equality. There are clear intersections between fat acceptance and feminism, as writers like Kate Harding have amply demonstrated, and there is also an unbelievable level of pushback when it comes to talking about fat in some feminist spaces; fat is bad, fat is bad for you, fat people are bad people.