Yes, many people tend to regard group identity as real and class identity as an abstraction because in this country class identity has always been ambiguous, and, more important, changeable(in peoples' heads, and sometimes in reality). You can shed your working-class membership in your lifetime (or so it is thought), but your blackness, gayness, femaleness etc. is forever.
Nevertheless, class and class struggle is more fundamental if you agree that capitalism is the term that best describes the kind of society we live under and want to transform into non-capitalism. Capitalism is possible w/o the oppression of gays, blacks, women and national minorities, but you can't have capitalists or capitalist society w/o workers. The class struggle is thus central to the struggle against capitalism in a way that others aren't. If you believe this, then you must also advocate putting class loyalty before group identity. There is no way around this. In class-struggle situations, female, gay and black bosses are the enemy, and male, straight and white workers are (at least potential) friends. Hillary Clinton and Barak Obama are in the political camp of the class enemy, and any appeal they make to gender and racial solidarity should be rejected out of hand.