Fat is still used as an insult -- which is why I don't think it's acceptable to shame someone for not wanting to be fat-shamed.
When "Fargo" actress Allison Tolman responded to Twitter haters who made jabs about her weight by stating that she wasn't "actually fat" and had just been wearing a parka coat for several weeks, some people took issue with it. Anna Breslaw at Cosmopolitan.com wrote, under the headline "Female Celebrities Who Insist They're Not Fat Are Part of the Problem": "It's absolutely true that the norm for women on TV is a size 0, but this problem of actresses asserting ownership over their bodies by replying that they're actually average rather than fat, as if being fat were the kiss of death, is hardly new."
Firstly, I don't think Tolman is fat by any means. Images of her on the Internet suggest that she is an average-sized woman. That point aside, I understand Breslaw's argument insofar as the word fat shouldn't be an insult -- because we shouldn't treat women differently because of their size. But we do.
If fat weren't an insult, women who identify as such would likely not have a problem saying so. If referring to someone as fat were the same as referring to someone as a brunette or tall or freckled, a woman's refusal to describe herself as such would be weird. But, collectively, we're not there yet. The word "fat" has power because the word "fat" has consequences.
People have been fired for being fat. Dumped. Divorced. Publicly shamed. While it's within someone's power to control how they react to being called the f-word, there is no shame in being hurt by an insult.
What needs to change is how our culture values people of different weights. Don't shame someone for feeling ashamed.