Interesting the definition of identity is simple:
the condition of being oneself or itself, and not another:
The condition of being oneself and not another, I would think the facts that make up oneself would be important in defining oneself as not another, facts like skin color, eye color, gender, etc,etc. Facts that are immutable, like skin color make us who we are and yet in the news is a woman who makes a statement like “I relate to being black” and we must redefine the idea of identity, one can have a sympathetic relationship with someone or something else (i.e; relate) without actually being that thing. For instance I have a sympathetic relationship with my pug Molly who has several medical issues, this does not make me a pug or give me any of those issues. In fact even if I relate to my pug I am still a human being with all the same conditions and identifying markers I had when I woke up this morning.
The characteristics of identity can be seen as those markers that make up the details (facts) of who we are. Some are immutable, I for instance am male, I have male genitalia and no matter how I dress, act or who I relate with the fact is I am male. I am also Caucasian, which implies my skin pigment is light in color, I may relate to black people and I do have several friends with darker skin but the fact remains I am still white. Each of these are immutable characteristics, meaning those characteristics that cannot be change or at least not changed easily.
Another characteristic that defines many people is wealth, some have it some do not and it is a fact that is dictated at the moment one is using the characteristic. Ones wealth may change, one day Bernie Madoff was a billionaire and the next after his trial he was penniless, this makes wealth a cursory characteristic or that identity marker which may change in time.
Each individual is defined in their identity by these markers, some are immutable and some are cursory and we can be defined by all of them but whatever the facts of these identity markers are is what we are defined by not by what we want these markers to be. One can demand that others treat them as if they are a woman but as long as one has male genitalia they are a man, genitalia being the defining identity marker and in this case it is immutable because to change this takes effort and money that is not afforded all people.
This is not to say that identifying as a group that one is not part of is wrong or should be not allowed, in fact as a free people it should be understood that we all make personal choices but this does imply a normal and that normal for immutable characteristic traits would be what we are brought into this world with, eye color, skin color gender, etc.
Sexuality would seem to be a cursory characteristic if one believes that they have a choice in what their sexual preference is and it could also be an immutable characteristic if it is found that homosexuals do not really choose their sexual preference but are born with it. The point of this writing is not to decide this issue but to point out there are known immutable character traits we all have and skin color is one of those. No matter whom we prefer or who we relate to our skin is a particular color and that will not change anytime soon.