Dog Folks has provided some very good information. In addition to that following is the law as it was when I was an ADA compliance officer for the state of Kansas.
Anyone can use disabled flagged sites but IF all disabled sites are full AND a qualifying person arrives at campground you can be required to move within a reasonable time period. Usually later the same day but I've also seen times that moving the next morning would be considered reasonable. It is pretty rare that you'd be asked to move but would be more likely on a big holiday weekend at a popular place. You can NOT be asked to move just because a disabled individual would rather have your site instead of another available disabled site. I have not heard of any major changes in the ADA regulations since I retired but there HAS been a huge change in how well it is enforced in many areas.