There is nothing wrong with engaging in education, ownership, or activities that are "privileged" by virtue of financial status so long as the child doesn't consider their privilege a right.
I think unknowingly, one of the best things my lovely wife and I did for our kids is to send them to the daycare located on the campus of the local community college. We live in a pretty typical Iowa community, fair to say not a lot of diversity racially, financially, or really any other difference, for lack of a more politically correct term, our area is about as "White Bread" as it comes, however, because the daycare was located on the community college campus, the mix of children there was simply perfect with children of widely varied ethnic, financial, physical, and educational backgrounds. My kids grew up blind to the differences because of that and carry that on to this day thankfully.
Knowingly, perhaps the best thing we've done is involve them in volunteerism, that tends to keep anyone humble and with a firm sense of gratitude in their hearts which combats any ill effects of being "privileged" quite nicely.
