“There could also be a new, modern interpetation. That people care more about where they belong in sociaty (whether they are chareidi, MO, yeshivish, and what percent of each) then what the torah wants them to do?”
I used to think that those things didn’t matter at all, but at some point I realized/decided that it does have some importance, and a person can’t ignore those things altogether, at least not in Eretz Yisroel. I tried to live my life that way for years, and it doesn’t work.
In addition to the fact that there are hashkafic reasons why it is important, it is also important for sociological reasons. Part of being a Torah Jew is being a healthy functional person, and part of being a healthy, functional person does mean knowing what your identity is. Obviously, your main identity is that you are an Eved Hashem, but you also have to fit into society, and part of your identity is knowing what sociological group you identify with. Just like being American, etc, is part of your identity.
That being said, obviously the focus should be on serving Hashem, and everything else is a means to an end. And a person should never get so caught on their labels that make decisions solely based on whether it’s a Yeshivish thing to do or a Modern Orthodox thing to do or whatever.