Wouldn't you reasonably assume he identified himself as being black somewhere along the line of things he identified with? Sure, he was a Starfleet Officer, a human, a captain, a diplomat, etc. But, based on his cultural upbringing isn't it reasonable to assume he also identified himself as a black man? The only alternative is to omit that fact and when there are mirrors and reflective surfaces... that is something of a challenge.
No, I
don't see why he would necessarilly see his skin colour as having any meaning in his self-identification. Why should looking in a mirror make him say "I have brown skin-
and this is significant"? First of all, in his society it doesn't mean anything. If there's no distinction between white, black, green, whatever, why would one see that as a mark of self-identification?
Well, the first thing I would say is that Sisko isn't reacting to his skin color
per se. What he
is reacting to is his heritage as an African-American; that is a culture that was categorized by its members' skin tones, of course, but being an African-American means far more than just a skin tone.
Yes,
Star Trek posits a future where there is no more discrimination, no more oppression, no more bigotry amongst Human beings. Everybody is equal; Earth is egalitarian.
But
Star Trek does not, and DS9 did not, depict, and
Star Trek has never depicted, a future where one's culture and one's heritage are meaningless. Pavel Chekov still cared about his Russian heritage (even if this was played for laughs); Kirk was proud of his heritage as an American (as evidenced in "The Omega Glory"); McCoy rather obviously considered himself a son of the American South; Picard was proud of his French heritage (in spite of his English accent!); Riker was proud of the fact that he was an American and an Alaskan to boot; O'Brien was proud of his Irish heritage; Chakotay was proud of his heritage as a Native American.
Now, to be fair,
Star Trek has often done a poor job of depicting a future where Human culture has not essentially been assimilated by Anglo-American culture. We didn't necessarily see someone who was proudly Chinese or Indian or Latino; characters like Sulu or Kim or Sato have tended to be depicted in a manner that mediates their status as non-Europeans by depicting them as people who are part of a more homogenized American culture that is often depicted as dominating Earth itself.
Nonetheless,
Star Trek has also always retained characters who are very proudly ethnic, and this has never not been the case.
If Jean-Luc Picard can define himself as a Frenchman in addition to seeing himself as Human, or if Pavel Chekov can be proud of his heritage as a Russian in addition to his Humanity, or if McCoy can see himself as a Southern gentleman
and an American
and a Human, then why can't Benjamin Sisko see himself as an African-American, an American, a Human,
and a Federate?
Why, exactly, is the idea that he still self-identifies as an African-American a threatening thing, unless you're trying to claim that self-identifying with an ethnic or racial identity is automatically un-egalitarian?
There is no reason to assume Sisko would ever identify as "black"- indeed, I never saw him do so in memory until this episode. Given the Benny Russell experience, it sort of makes some sense, but it's still a surprise.
I don't think so. He was an African-American Human Federate, born of two African-American Human Federates, who married two African-American Human Federates, who maintained an interest in his culture's and sub-culture's history (both American and African-American) all throughout the series (as indicated by his knowledge of American history and his collection of African artwork). It may not have been as overt as Picard's switching into French to curse or Bashir singing "Jerusalem" whilst drunk and playing the Battle of Britain, but it was always there.
And, frankly, I think that the world would be a much sadder, much more homogenized, and much poorer place if African-American culture were to disappear or be subsumed into a larger culture. Diversity and multiculturalism within an egalitarian, democratic framework are what it's all about.
) For the record I do not think you are a racist for not liking the scene. 
(Granted, I haven't seen a lot of movies he's been in, but that was actually the first I saw that wasn't DS9.)
