How much can a 4's fear of shame and humiliation mask as 6's need for approval? How much approval do 4s need from others? Do 4s need approval at all? How much is 4's self confidence influenced by how other's view them?
Personally, my own struggle with the 4's notion that something is inherently wrong with them was more externalized and objective, and as such has a lot to do with the responses of other people. I was a kid with anxiety and panic disorders - that something was off about me wasn't just in my mind, but something teachers IRL told my parents and kids told other kids. Other people treated me that way, and that would be fact whether I came to believe it myself or not. Anxiety may be incredibly common and easily treated, but the timing of its onset was way more destructive than the thing itself ever could have been - kids are more limited in their abilities to tell illusion from reality, to hide pain, to explain themselves, and because they are under the legal care of others, to just protect themselves from stigma in all sorts of ways.
Because of that, I did learn to place importance on what others think in areas where practical/material things may hang in the balance. For instance, one cannot get a job until an interviewer looks upon them and their skills favorably, but then if their boss hates them, they probably won't be keeping it for very long. Another example, age and health problems affect people with and people without a social support system very differently. Also consider people who have infamously lost their jobs or received death threats because enough people disliked something they posted on the internet. The list could go on. Other people can come to you with opportunities if they think you can handle them, or try to take control of you if they don't find you self-sufficient enough. One time when I was in school, I got an A in a class but was still held back for a year because the teachers thought I was too stressed by the class and couldn't hack more difficult material emotionally. They would not reconsider when asked. That's the power of what people think, although perhaps magnified by being a kid at the time and having less autonomy. Where I do have unwarranted concern over what others think (like thinking some relationship poses a practical risk where it realistically does not), it probably is because those fears go back to childhood situations where I had less control than I do as an adult.
On the other hand, in areas of independent and harmless self-expression, no, I do not care what others think of that. I don't feel a need to appear like others or to fit in for the sake of belonging, or otherwise for its own sake - only if the apparent differences could interfere with my success (it can be really maddening how often that is the case, though, how much interdependence can creep into things where it may not be necessary or wanted). Outside of that, it doesn't matter. In the end, it doesn't matter, either - where I compromise, it is only as a means to an end where over time, such compromise will be required of me less and less because of the payment I made earlier on. The definition of success is a collaboration between myself and a society nobody can escape, and I may give certain systems just enough of me so that they will leave me alone. To rebel would be to have that stuff up in my life way more than it needs to be, so I don't.
I don't sit easily with the feeling of being defective or lesser; I need to prove that feeling wrong in such a concrete, active way that it gets shut down with the power of material fact. That's what my part of success means - if I can't get rid of a defect, it must be transformed so that it is part of why I excelled at something. It's perfectionistic - difficulty letting a shortcoming just be a shortcoming. Feelings like that can come from within, or they could come from other people's thoughts and words in the past. Either way, if a success is visible, that does give it some extra pleasure.