IMO, right-wingers (a group that includes me) tend to have a blind spot when it comes to "white privilege." Admittedly, the term itself is probably poorly chosen, but the phenomenon that it describes is pretty obviously real.
You're right of course that Lebron's kids are probably going to have a much easier time going through life than my kids. But that's not the point. When people talk about white privilege, they don't mean "Every white person has it easier than every black person." That would be silly, and pointing to Lebron would be a good and easy refutation of that argument. What they mean is more like "All else equal, black people tend to have a harder time than white people," and that argument seems to be quite clearly true.
If I imagine a guy who is exactly like me -- an educated, middle-aged guy with a conventional family life, a cushy upper-middle class job, healthy IRAs, chiseled good looks, etc. -- only he's black, his life is going to be at least a little harder than mine. He'll get stopped by the police more often than I do, he'll have his authority questioned way more often than mine is, he'll constantly walk around wondering whether every sideways look directed his way was due to racism or whether it something more mundane, etc. None of those are back-breakers, but I don't doubt that they add up over time.
Maybe a better way of thinking about it is to think of it in terms of overlapping distributions. In the "Biden vs. Girls Sports" thread, we talk a lot about how men are better at sports than women. We all understand that that doesn't mean that every man is better than every woman. It just means that if we think of "sports ability" as being a bell curve, men have a higher mean ability than women, but their distributions overlap. Some women are better than some men, and a few women are better than most men. But no women are better than the top men, and all women are worse than they would be if they were male, all else equal. Conceived that way, it would make sense to talk about "male privilege" in the sporting world, because men collectively are just better at sports in a broad, population-level sense.
"White privilege" is basically the same thing. White people have it easier in life in a broad, population-level sense. I see that as about as controversial as sex differences in sports, which is to say that it's not controversial at all.
Obviously the solutions here are different, but the basic concepts are pretty similar.