It's a really difficult situation for both sides. I think the strife stems partly from a widespread delusion on social mobility in America - the myth of meritocracy. We are led to believe that the poor could become rich if they just worked really hard. Those who fail, we are told, did so because they were too lazy. The reality is that Horatio Alger stories are rare, for the poor of all races.

Due to their shared history of abuses at the hands of Whites, now mostly dead, impoverished Black people identify themselves more in terms of race than economic class. Like most Americans, they accept that hard work is required for social mobility, but clearly something else must be required as they likely know many people who work hard but must run as fast as they can to stay in the same place. They may well conclude that they can't get any "lucky breaks," or whatever it takes to get ahead, because nobody will give them a chance due to their race. As you might imagine, this must be frustrating, and may cause them to see America as a land of hypocrisy. Well it is, but that's not exactly why. The real reason is that upward social mobility in America is uncommon, and the way our society is structured makes it extremely difficult to get ahead. Thus people acquire financial goals and expectations that don't mesh with reality, and this is extremely unhealthy for individuals and society.

One tool that policymakers have tried to remedy the effects of classism/racism (or sexism) is affirmative action, but this is a double-edge sword. It may diminish the self-esteem of minorities who were accepted/hired for reasons other than merit. It also makes Whites bitter, and may encourage racism. Lets say their kid is trying to get into college, and they perceive that the spot has been taken by a less-qualified, though disadvantaged, minority applicant due to affirmative action. It's a real problem because it rarely boils down to merit in America. Especially affluent Whites can pay for an amazing education at a private high school. Middle-classed Whites have an edge too, as public schools in America are funded by localized taxes. Thus schools in poor neighborhoods can't offer the same education.

Education is increasingly the only way to get out of poverty. When America was more industrial-based, it was possible to be trained on the job without a high school education and in many cases, still be middle-classed. This is much less common today. While schools are not formally segregated by race now as they were a half century ago, they are even more segregated in terms of economic class. Education is increasingly expensive and few state and federal resources go to help students of all races to achieve it.

Basically, ameliorating the "race problem" is going to have to start with an education system that allows an inner city kid to get an education that is of a similar quality to that of at least a public school in an affluent neighborhood. Schools' funding will need to become a priority, and it will need to be equitably distributed.