Let’s make these assumptions:

1. All the slots in a desirable institution are held by white men, most of whom are wealthy, and none of whom are out as gay. That would (for instance) be a rough description of the student bodies of Harvard, Yale, and Princeton ca. 1960.
2. Wealthy, straight, white men also tend to hold biased views of the other groups.
3. Most people want their children to have at least the same advantages (in both absolute and relative terms) that they’ve had.
4. People with social, cultural, or financial capital are quite good at obtaining advantages for their own kids. Just for instance, after the collapse of the Roman Empire and the demise of paganism, France was run by Frankish bishops instead of the Roman landlords who had dominated Gaul. But it turns out the bishops were descended from the landlords, because the Gallo-Roman elite figured out how to weather even the profound disruptions of AD 300-600 and put their own sons on top of the new order.

Now let’s envision that the biased views mentioned in #2 (above) go away. Wealthy, straight, white men develop genuinely respectful, appreciative, egalitarian views toward all others. Meanwhile, the other groups come to believe that they have equal potential and rights, rather than internalizing bias against themselves. What happens?

Most women and most gay men are children of straight men. Therefore, if advantaged moms and dads simply form the opinion that their own daughters and gay children have fully equal potential and worth, then they will demand spaces for those kids at the top of the social scale. Social outcomes should change quickly as a result of attitudinal changes. The only obstacles are: (1) persistent bias, which may become implicit and subtle, (2) leftover policies and structures that discriminate, such as policies regarding parental leave, and (3) the reluctance of incumbents to yield their own places. To the last point: you wouldn’t expect tenured Ivy League professors or US Senators to resign to make room for women, but you would expect the gender ratio to improve with generational turnover, as long as attitudes truly change.

In contrast, most people have the same race/ethnicity as their parents. Therefore, even if all the white parents who dominate the preferred slots in a society come to believe that people of color are fully equal and entirely welcome, if they also succeed in obtaining slots for their own kids, then racial demographics will shift slowly, if at all. Attitudinal change will have little impact on outcomes. Absent major pressure from outside the system, all you’ll see is slow, incremental change as each family of color that makes it to the top holds a spot for its own kids.

As for class advantage, it presumably consists of having a better-than-average chance of attaining a desirable social role for yourself or your kids. In the list above, I assume that a society provides highly some desirable social slots (such as places in the student body of Harvard, Yale, and Princeton), and that parents confer advantage in obtaining those slots. For instance, US parents who have attended college have an 82% chance of sending their own kids to college, versus a 36% chance for parents who didn’t complete high school.

But both of those circumstances are variables, not constants. A society can offer a steeper or gentler gradient of social advantage, and the correlation between parents’ and children’s advantage can be larger or smaller. In Continental Europe and Canada, colleges do not differ nearly as much in reputation and resources as they do in the US and Britain, which means that it matters less where you enroll. However, it is worth noting that even in Sweden, with a century of social democracy behind it, today’s upper class is substantially descended from the 17th century aristocracy. But Swedish women now earn 95% as much as Swedish men and fill 43% of the seats in the legislature. In Sweden, new attitudes toward gender (and sexual orientation) led to deep changes in individual choices and social policies. But new attitudes toward class didn’t dislodge Sweden’s most advantaged families.