This feels a bit off to me. Most of the people I've met who are really passionate about fighting discrimination against LGBT people have also been very interested in fighting fatphobia (discrimination against overweight people) and ableism (discrimination against the disabled). I think the difference may be that accommodations for disabled and obese people are often more difficult or expensive, although I don't have numbers or anything to prove that.

Accessibility for the disabled is also less of a "culture war"-type issue, so progress (or lack of progress) doesn't tend to be as visible.