How culture change is an interesting topic. From what I can see myself in regard to racism, efforts to change culture occur in practically every place. In media, in news, in politics, online, in advertisements and so on. However I would say that before any such methods there need to be an initial work that brings the issue into the public mind. Social inequality is not a problem which currently is seen as a problem, and so there is where such change must start.
Economic equality and social safety net are very important overall, but in this aspect there do exist a small paradox where increased economic equality increases social inequality. The causes for that is from what I see a still researched topic with multiple competing theories. The one I suspect is closest is that when economic equality increases, you get more instability in the social hierarchies, resulting in people putting higher value onto cultural cues.
As for the third obstacles, as with race, you don't need to explicit state economic status in order for people to guess it through proxy. Job title, clothing, where people live, all gives cues about money. There is a reason why tanned skin is still seen as an proxy for wealth, and why non-tanned skin was seen as a proxy for wealth back in a time where the majority of people worked as farmers.
If I look at the future and especially at places like China, there are additional tools for culture change which could be used for both good and bad. AI companions and citizen scores could be used to influence a population towards a culture change. A lot of technology is written to influence consumer behavior, and the same technology are already being used to influence political behavior. Influencing culture would not be that far jump, and it could potentially do so at a speed yet unseen outside of war.
