Identity is bad, except for your mandatory socialist awareness
It really is something to watch the most bitterly divisive President in American history lecture other people about identity politics. Particularly if you step back from the identity-politics gambits made by Obama himself over the years - get in their faces, punish your enemies, bitter clingers, "you didn't build that," and his constant insinuation that people who don't support him are motivated by racial discomfort - and look at what the various arms of his campaign were doing. A great deal of his 2012 polling strength in certain districts was marshaled by telling minority voters that common-sense voter ID laws were a racist conspiracy to suppress them.
"Identity politics" are just fine with liberals, provided they approve of the identity in question. What's the divisive propaganda quotient in the religious schools Obama suddenly seems to hate, compared to what gets dished out in the public schools he'll do anything to keep kids - most especially including minority kids - from escaping?
As you noted, even a fairly extreme sense of identity is largely harmless until political organization and State power are added to the mix. No one has trouble living next to Amish communities with a powerful sense of religious identity, because the Amish are not interested in accumulating political power so they can use the force of government to impose their beliefs on anyone else.
There's something deeply creepy about Obama's description of "the choices ordinary people make that divide us from one another." We're supposed to be free to make those choices, and yet still respect the rules of civic order. The founders of the American republic believed this was a universal principle, applicable to all mankind, not just an American point of law. And while the situation in Africa is quite different from the United States, there are some essential similarities as well. We have tribal identities here, based on cultural choices and geographic location. Our tribal clashes tend to be far more good-natured than what President Obama was speaking out against, but alas, there is some violent friction as well. We've also got a good deal of voluntary racial segregation, from cities to college campuses, and it's not all happening at the whim of white people.
Want a good current example of bitterly divisive American identity politics? Take a look at the "Stand With Wendy" personality cult of abortion extremists. That's nothing but an aggressive declaration of identity-based warfare against a hated Other. The position Wendy Davis "stood for" has something like 16 percent support from the American people. I suspect a lot of the people bellowing "Stand with Wendy!' on Twitter would vomit with revulsion if they got a good long look at the hellish procedure she's championing; they would howl in outrage if any other big-bucks industry behaved like the one she's defending. But they deeply dislike the people on the other side of the argument, and they love having a hip, cool icon they can empower with their focused bitterness. Barack Obama, who is another such icon, has no problems whatsoever with this outbreak of identity politics; he openly supports Davis.
Life in a constitutional republic involves getting along with others without sacrificing your identity. Life in a socialist basket case involves accepting an identity custom-built by the hive mind of the State, which has some very particular ideas about what its people must believe.