Society has a discrimination problem. It would be nothing short of a miracle if the people on AirBnB were different from everyone else in this regard. (It'd be like expecting Facebook users to be free of discrimination, and then have news articles implying that Facebook is to blame because there are a couple idiots among its users. There is a recent Harvard study that is decidedely weird in the way they pitch their findings.)
In fact, AirBnB actively promotes diversity, and not only in statements, but also in the way the site works. For example, you rank higher in search results if you turn on Instant Book. (I'm not a big fan of instant book open to everyone because I'd like to make sure the guest has the right expectations and understands the AirBnB concept, but you can also turn it on only for guests who have some completed stays with positive reviews.) Anyway, Instant Book is a sure-fire way to avoid discrimination.
I do have a thought about going even further.. for example AirBnB user profiles could allow people to enter their ethnic background. (hear me out now. 😉 ) It wouldn't be visible to anyone else, just for internal use. And then hosts who have shown to welcome guests from diverse backgrounds could get a little extra boost in the search results ranking. (The algorithm will take some figuring out but it's likely possible)
And to state the obvious: for a host to use ethnic background or nationality to decline or favor guest bookings is completely nonsensical. You really can’t tell what a person will be like in terms of being tidy or following house rules based on that. And that’s from personal experience, taking hundreds of bookings from all over the world. In fact I like scrolling through my reviews and seeing people and languages from all over the world. It's actually a great thing to meet so many different people from different countries, it's the next best thing from travelling the world yourself!