While I completely agree with the premise, I see several obstacles:
1. How would you change culture on such a massive scale?
2. Given the poor state of a social safety net in the US, economic problems can very well be a real strain on a relationship, causing practical problems that might not otherwise crop up, killing relationships that might’ve otherwise survived. I think providing a better social safety net would go a long way towards helping solve this problem
3. Money is already generally not a thing shown on Tinder profiles, and yet the Tinder Gino coefficient is much worse than most real-life countries
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.
There is no more undateable men than there is an undateable skin color, especially if we are talking about portions like 20% of a population.
Ask what makes those people undateable and the answer will be rooted in culture.