In the comments, Evildoer claims, "Socialism is also identity politics. When Marx described the process as moving from a class "in itself" to a class "for itself", isn't that exactly "the politicization of identity"?"
Socialism is not identity politics. Identity politics describe the world in terms of being: people are male or female, black or white, Californian or Welsh, Coke drinkers or Pepsi drinkers. Socialism describes the world in terms of doing: the capitalist class controls the world's wealth; the working class works to survive. That many people do not recognize their role under capitalism has nothing to do with identity. It only has to do with ignorance that is promoted by the ruling class.
Identity politics see the world in fixed terms: race and gender cannot be changed, and their concept of class is feudal, so birth is very important to what you are. But socialists see the world in mutable terms, tribal rather than racial.
Mind you, this view of capitalism is not unique to socialism. Many capitalists recognize that under capitalism, what matters is your relationship to capital. Which is why socialists and capitalists see Obama as being true to his class, but identitarians see him as a traitor to his race.