"Not caring what anyone thinks" can be itself, and not so subtly, a form of approval seeking. We all know we're supposed to be this way. Society says it's good. According to the theory and sometimes in practice, people will respect you more if you don't care what anyone thinks, if you go and do you. But not caring what anyone thinks is reactionary, and it's in essentially all cases a lie. If you really didn't care, you wouldn't be making a big kerfuffle about it. (Nor would it be healthy or sustainable.)
What does it take to find the humility to say, "I do care what people think, but I'm the one charting my course. If some people like what I do, that's great. If some people don't like it, then I'm sorry or possibly not sorry. But I'm the one living this life, not anyone else. I choose." Is that very difficult? It's certainly more honest. All this posturing and convincing yourself that you truly don't give a fuck what anyone thinks - honestly, I find it sounds very gullible.
But you wouldn't be interested in that, because you don't care what anyone thinks.
Hell, you don't even care what you think. You're an anyone. What does coherency matter, anyway?
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It's normal and human and healthy and constructive to care what people think. There's no good excuse for ragging on people who want the approval of others: you do also, whether or not you're putting on a big show (or blank facade) about not wanting approval. We evolved to be like this, and it holds society together. Good grief, people will devote themselves to cultish ideas at the drop of a bowling pin.
I don't find it brave or intelligent not to care what anyone thinks. It seems like a deficiency that might in some cases work in your favor - for example, if you're a hermit, or you spend all your life in the same room doing mathematics.
What is sensible, though, is taking charge of your own responsibility to chart a course through the universe that's available to you. That's you. You make those calls, in the end. You can care and still choose for yourself. Caring what you think doesn't mean I must do what you say. Since when did that even look like an equation?
If you tell me what I wrote above is highly delusional, I will care - I will take it seriously and think about it. But I'll probably end up concluding that it isn't delusional. No need to get reactionary. No need to declare my allegiance to the flag of not caring what anyone thinks.