To have an identity (or group identity) built with it. Describe yourself in as few words as you can in a way that other people can tell it's you and what you're like. You know what else besides your skin color or political affiliation is bound to be there? Your name. Would you find a name scientifically tenable or non-arbitrary (whaterver that means) as a part of an idenity? Probably no. But mispronounce someone's name and you'll see how touchy people get.
I have no idea what you're talking about but I'm pretty sure that you're mixing completely different concepts, identity, group identity and personality. I would call the former, at least in the way you describe it here, personality - and would definitely disagree that the colour of one's skin is part of it. I also have no idea why, for example, political affiliation should be part of an identity, something that can change (at least in theory) rapidly and frequently. Does changing your political affiliation also change your identity? Is someone who, for example, voted for the KSČM and then voted for SPD or ANO not identical with himself anymore (or does he just change his identity, and where's the difference)? Is it sufficient to, another stupid example, go to a tanning salon to change one's identity? What's the purpose of identity other than to identify someone?
Just standing there, maybe pointing at myself, is completely sufficient to identify myself to others. No words needed. Even when I'm gone, the people could still identify me as 'the person who just stood there'. If I told them some name, it doesn't have to be my own, they could just use that in order to unambigiously identify me. Seriously I have no idea what your point is and even less what that has to do with a movie cast.
As can be seen you also lost me completely with the name example. That we seem to meet differently tempered kind of people is the only thing I gather from it.
You are still ignoring the noticeableness, claiming it to be arbitrariness. Al Capone's biopic can be shot with a Mercedes-Benz 500K and it can be shot with a Dodge Charger. Both are wrong, one is wronger.
I vehemently disagree with the notion that something can be "wronger" than something else.
I don't think that I'm ignoring the noticeableness, I tried to dismiss it to some degree with the example of a blind person. What I would claim though is that the things you notice 'more' are actually the result of you to judge them as more important (on whatever that judgement may be based on). And that that assessment is ultimately arbitrary (or that I see no valid reason why the skin colour should be deemed more important than anything else, or important at all for that matter). Again: I'm talking in the context of movie casts (as in: movies whose primary function is, I think, to entertain (even so-called historical ones), not inform, especially in comparison to documentaries, and, to a lesser degree, biopics).