Despite having a certain personal sympathy for identity politics of race and gender, Obama is much too much of an astute and ambitious politician to let himself be overwhelmed by ideology. Yes he is a Democrat and tends to go a bit left (as Dems, tend to do), but he also wants to win elections and is smart enough to know that he will not get very far if he consistently pursues policies of the far left which are out of touch with the mainstream. Most of Obama´s policies have either been centrist or mainstream Democratic left of center.
During the election the image often given was of an innocent and idealistic Obama, whose only fault was that he might be a bit too naive. In fact Obama is a very skilled and aware politician who calculates his message according to the crowd he is dealing with, which is why during the last election he could often appeal to business people, centrists, leftists, etc. In the Gates incident his first outburst was to call the police stupid which showed his real feelings. Soon whoever the politician in him realized his error and arranged an nice chat over a beer to smooth over the whole incident.