I care a lot, personally. It's not just appearance; it is, but that's half of it. The other half is physical comfort. I want to look the way I want to look, because I like myself better that way AND I'm more physically comfortable that way. I am also more self-confident when I look the way I want to, especially in professional settings. I guess that's kind of a given, but yeah. I care about that a lot. I refuse to leave the house with curly hair. I hate how it looks and I hate how it feels even more. I am only comfortable when it's straightened. It looks dozens of time better and feels dozens more times better.
Same for facial hair. If I could get rid of it permanently, I would do it in a heartbeat. Not just the hair on my face, but all over body hair, as well. It's extremely gross-feeling and highly discomforting. I want all of it gone. That's not outwardly visible except on my face, so it's less pressing appearance-wise, but it's highly pressing comfort-wise. Unfortunately I can't do anything about it right now. The best I can do is take care of my hair and shave at every earliest possible opportunity. I have a very strict routine for that. I shave every three days; any earlier and I get lots of cuts, so I have to wait three days. I tend to straighten my hair whenever I feel discomfort, but I try to make sure I do it after showers because it always turns out best that way. This is what I do to feel good about myself and to feel physically comfortable.
All of this I do for myself. My own comfort and happiness is the priority here. I do care how others perceive me, but it's more of wanting them to perceive me the way I want them to than anything else. I don't think "I wonder how they see me", I think "I hope they see me the way I tried to present". I'm not sure how much of a distinction that really is, but the distinction matters to me nonetheless.