I see your point. I guess for something like this to work, bigotry/racism/whatever would have to decrease in popularity to the point where you would be shunned harder if you were a bigot than if you were a person who openly objected to bigotry. We may not be there yet, but I do feel optimistic that we will eventually get there. Things were much worse only a short time ago. One thing that makes this ("this" being the idea of the market “handling” the problem) harder to accomplish is the fact that many people who may not be discriminatory themselves tend to have a passive attitude towards discrimination as long as it’s not happening to them. For example, many white people aren’t racist, but would they all agree to boycott a store that was openly racist towards black people? Probably not.

I think much of the problem is that these toxic effects aren't being created by overt bigotry, but rather by cognitive biases. The people rescinding reservations are doing so out of loss aversion, which is a very powerful human impulse. We're also powerfully geared to think differently about outgroups than we do about ingroups, which makes it easy for us to believe that there's a higher degree of risk in allowing a black family to stay in our house than a white one.

Social stigma might blunt these effects but it's unlikely to eliminate them any time soon. I bet a lot of the people who (effectively) refuse to rent to black people don't think they're the slightest bit biased against black people. They're not keeping track of their individual decisions about rental applicants, and they can easily let their brains fill in the blanks to tell them there were all sorts of negative signals they picked up on when declining reservations.

One of the reasons things are much better now are because laws against discrimination change what is socially acceptable. As regards the market handling it, we needn't speculate, just look at the actual history of racial discrimination in the US, from white-only diners to schools, that was only overcome by direct government intervention.

You can be optimistic all you like that we'll "eventually get there" (I'm not) but optimism doesn't do much for people whose rights are being infringed today.