These indicators don't necessarily show that there's anything ingrained at all, or that there's any active privilege now except for historical circumstance. It could just be that the U.S. doesn't have the social mobility that we like to pretend it does--history matters. (And, indeed, it does matter; the U.S. does not score incredibly well on social mobility; see e.g. https://en.wikipedia.org/wiki/Global_Social_Mobility_Index#Global_Social_Mobility_Index_(2020))
The indicators do show that something was seriously messed up somewhere. Undoubtedly there have been a lot of past actions and attitudes in the U.S. that were utterly inhumane and shameful--but just as undoubtedly, those have gotten massively better.
As an example, in Adams County, North Dakota (https://en.wikipedia.org/wiki/Adams_County,_North_Dakota), the per-household income in 2010 was $36k. Adams County is 98% white. Do we conclude that there is pervasive structural anti-Adams-Countyism? Or do we perhaps look for another explanation?
Furthermore, your numbers don't all even tell the story that you say they do. You say "White people earn an average of $71,000 a year" but your chart shows households! Households aren't people. Do you know whether there are differences between, say, whites and blacks when it comes to households? (Hint: there are.)
Okay, so we need to look at _personal_ income because you want to talk about people (not households), yes? These numbers are a little harder to find (it's easier to measure a household because it has a mailing address, and Census workers will show up there too...), but https://en.wikipedia.org/wiki/Personal_income_in_the_United_States has a good overview. The latest data reported (2016) shows these median personal yearly incomes: $40k for white males, $25k for white females, $30k for black males, $22k for black females. So, okay, 60% for males looks pretty bad still; point still stands. What's the deal with females, though? That's like 90%. Not ideal, but not nearly so bad as 60%.
Fortunately, we can dig deeper on that same chart (albeit with slightly older data--2006) by breaking things down by education level. For people with a doctorate, who are working full-time (and really, if you have a doctorate you _almost_ always can be working full time if you really want to be), whites earn $77k and blacks earn $73k. Wait. Where'd the disparity go? Now we get 95%. Oh, and Asians earn $91k?! (If we look at all people whether or not they're working full-time, it looks different: $71k vs. $61k vs. $70k...apparently there are differences in amount of work too, but this can depend a lot on personal choice not on opportunity.) If we look across other education categories, it's pretty much the same thing: there is still a gap, but it's way smaller--black individuals of the same educational attainment earn 85-95% of what their white counterparts do (with the smaller ranges appearing at higher educational attainments).
But the real story is this: the typical person with a doctorate earns $70k. With a bachelor's degree, $40k. With only a high school diploma, $25k. Even now, blacks only get doctorates at 75% of the rate of whites. Bachelor's degrees at 90% of the rate. Historically it was worse--rates of having a bachelor's are only 70% among blacks of what they are among whites, and of a doctorate only or professional degree only half. That's most of where your huge income numbers come from! Attainment now is better than it was historically, but there's still a gap. As long as that gap persists, and as long as we value education and skill and talent over the lack thereof, the income gap will continue.
Education and attainment needs focus. Real, substantive focus, where people are valued and invested in in the long run, not just a few sound-good feel-good measures that people can take to make it seem like they care. This gives a double boost: first, a direct boost by increasing one's value, and second, an indirect boost by vaulting one into a situation where systemic barriers appear as if they're probably lower (by virtue of the smaller income disparity).
The United States, as I said, has a problem with social mobility. If you look at breakdowns of this by race, e.g. as in http://www.equality-of-opportunity.org/assets/documents/race_paper.pdf (go to Table 1 on page 57), you can get an idea of how this works. If your parents are in the bottom 20% of the income distribution, and you're white, you have a 28% chance of having the same fate (if it were random where you ended up, you'd have a 20% chance). White people at the bottom tend to get a bit stuck at the bottom. But if you're black, you have...the...same 28% chance. However, this hides a huge disparity--black women have a 20% chance, as if they get an even chance like you'd imagine if mobility was perfect. But black men have a 38% chance to stay stuck. This is awful, depressing. (On the other hand, black women get a break compared to whites in that category...maybe small comfort compared to the crap their brothers have to survive, but take blessings where you can find them.) And if parents make it to the top 20%, their children are still only 24% likely to stay at that level (less than whites), barely better than chance--but at least it's equal for men and women.
This is a deep problem. But it's not an insurmountable problem. If you look at the rates for Asians, you find that they just don't stay at the bottom. If Asian parents are in the bottom 20%, their children are 28% likely to end up...in the TOP 20%! If the parents are already in the top 20%, the children have a 50% chance of keeping that status. This is vastly better than white parents manage (bottom -> top is only 11%, and even staying in the top is only 37% likely). So, with attitude / culture, presumably, you can beat the system. There is mobility, but it requires something that apparently Asian subcultures have figured out (at least before staying in the U.S. for too long--there's data e.g. in Table VI on page 66 indicating that 3rd generation Asians don't overperform as much). What is it? The cultural focus on education seems like the obvious candidate to me.
So, overall, if you dig into what is actually going on, one big message--not the only one, but the biggest that I've found by a substantial margin--is: focus on education. Focus on accomplishment. That's where the biggest gains are.
Also, don't make catchy graphs with misleading numbers. People who feel you're on their side may cheer, but anyone against you will find holes in seconds, and anyone undecided is liable to conclude that you don't know what you're talking about and will spend their time somewhere else. So dig deep, explain the graphs for what they are or make better ones that really get to the core issues, and there's still plenty to talk about.