The difference is that people with the issues or characteristics you mentioned aren't having their rights infringed upon and discriminated against by politicians and hate groups.
The people with the characteristics you mentioned are accepted. Are you referring to someone being bullied because they're tall or short or different in whatever way? That's not really as big an issue if a small group doesn't accept an individual because they're different but when it happens on large scale to a large number of people is when the issues arise and when people are treated as less of a person because of something they cannot change.
First, I didn't talk about rights I talked about acceptance. You think the groups I mentioned are accepted, really? I haven't heard about people not being hired because their gay, but I have heard about people who weren't hired because they weren't good looking enough. If people can accept every different human being, then they will be able to accept gay people, but until then it won't be possible.
P.S I think that the group that is bullied the most is the people who have weight issues, not the gay group. Just look at a school in your neighborhood