Folks who think that we are living in a "post-racial" America are mostly racists.
I have encountered several kinds of racists in America and understand that all these categories of racists exist in America at this very moment.
Firstly, you have your die hard, unapologetic and admitted racists in the KKK and other white supremacist or separatist organizations or who agree openly with the organizations about the inferiority of other races. Fortunately, these are few in number.
Secondly, you have folks who believe in the inferiority of other races but are aware that it is inappropriate to express their beliefs outside of the most intimate circles. There are a crapload of people like this. Everybody knows somebody like this. They whine about "political correctness" because it makes it harder for them to express their odious views.
Thirdly, you have folks who would deny that they are racists but who actually are, often without realizing it. They don't even know that their viewpoints are racist, and they reckon that as long as they aren't overtly hostile toward someone from another race, they aren't racist. Yet they believe in the inferiority of other races and wonder why they don't just get up off their lazy asses and stop whining about discrimination and playing the victim. These people just don't get it. They don't live near anyone of the other race, go to church with them, or socialize with them, and they don't have any idea about the circumstances of people in that other racial category other than to note that they are relatively poor, often in trouble with the law, and scary in large numbers. They are pretty sure that whatever problems the other race has are their own fault.
Fourthly, you have folks who claim not to be racists and who reckon racism is a bad thing that ought to be eradicated, but they are sick and tired of "white guilt". They want other races to get over it and move on to a post-racial society and reckon that the other races are the obstacles to this. This is because they fail to understand that nobody cares whether they experience "guilt", only that they acknowledge the reality of discrimination and racist attitudes in the country and the damage that these do.
Fifthly, you have folks who harbor unconscious racist ideas as a result of their upbringing and living in a racist society. They may well deny being racist and hate racism and acknowledge its harmful effects in society, but there's a little part of them that reacts negatively whenever they see an interracial couple, for example.
Sixthly, you have folks from the fifth category who admit that they almost certainly harbor some unconscious prejudices and are working on dealing with them. When it comes to racial justice, however, they don't really go out of their way to change things through the way they live.
Add these up, and I will bet you will have a supermajority of white Americans.