A point worth mentioning is that white people in the US tend not to really think of ourselves as white most of the time. I want to believe that ultimately race shouldn't matter, and that's a goal we should strive for, which means only focusing on race when you're dealing with actual racism, with law enforcement for example. I went to a very liberal middle/high school and was taught that I should flagellate myself for being white, and I did at first, but then I came to reject that. Then when I saw people at my college insisting that I should support various stupid proposals by some minority students to benefit minorities at the expense of the college as a whole because they were minorities, I felt acutely white, and angry about it.
I ultimately settled on the liberal position of "we need to treat everyone equally," which I believe is still the consensus position in this country. But I'm sure it helped that I knew minority students and faculty who also took that position, and who actually stood up to the activists demanding absurd things. If I felt like all the minority members of my college were hostile, would I have harbored racial resentments, the way many Trump supporters seem to?
Now there are issues where racial awareness is important and those are worth calling out even if makes white people feel attacked. I'm always amazed at how many people don't believe the police and the courts have a racism problem, and I'm sure it makes a lot of them feel attacked. With these people you probably are exposing latent racism. Yet more Americans support Black Lives Matter (the modern equivalent of MLK) than oppose them, and this is despite the conservative media falsely portraying them as radicals who demonize white people and want special treatment. (MLK similarly suffered people falsely calling him a communist plant.) It shows that a reasonable message of "the playing field is slanted, we need to correct it" can reach people.
However the wrong strategy is to actually demonize white people and demand special treatment. This is what I often encountered in middle school through college. In the short term you may win over naive college students, Marxist professors, and timorous administrators, but in the long term you risk alienating people, people who actually do want to do right but don't see "doing right" as tilting the playing field against themselves. When you demand that white people look at everything through a racial lens and tilt the scales in your favor, you run the risk of achieving the first without the second.