(be forwarned: WALL OF TEXT)
Fat acceptance is an extreme response to another opposing extreme: fat shaming and the promotion of the unhealthy skinny body. Really, both extremes are not good. Obesity, as a whole, should not be accepted as healthy and ok, but neither should fat shaming being a motivating method to get people to lose weight- since it doesn't work. And we all the know the sad stories of girls being affected by the overwhelming image of photoshopped models in magazines.
But we also can't generalize all obese people either, not all obese people are fat and lazy. A lot of them get obese because of medication, and try like hell to lose the weight with very little pay out, but are unable to get off the meds.
That being said, while I feel for people who are obese via meds, I do not feel for the people who are obese because no excuse. Obesity is a huge problem, because its extra weight that gets put on the joints and feet that makes being active difficult, and you need to be active to live a quality life. Obesity doesn't cause heart disease or diabetes in everyone, it didn't for me, I just had a problem with my knees and feet- and that was reason enough.
But there's nothing wrong with being overweight, there are a lot of people who are healthy, active and look good being overweight. The difference is, they're only 10-30lbs over weight as opposed to being 50+ lbs overweight. The problem is, a lot of fat-acceptance obese people, try to put themselves in the same category as people who are only a little overweight- when they're not in the same category.
So, to answer your question: if the obesity can be fixed, then no, society should not have to accept their obesity. But on the same token, should not be shaming them either and shoving anorexias in their faces.
But don't generalize and assume either.