It would obviously be politically unpalatable, but in a way it might be better if say AirBNB implemented support for discrimination on their platform. It's obviously something that exists, so reifying it into the formal system should make it easier to optimize away.
If you want to participate in social media (which you have to, some people won't communicate any other way) you've got to accept that not everyone views your privacy the way you do.
And even of it did work, it wouldn't solve the issue since discrimination based on name can happen just as easily for people with obviously-black or obviously-Islamic names.
If I can't choose who to allow into my home, I am not using AirBnB as a host. I am confident that almost everyone shares this sentiment.
Imagine if AirBnB required you to let anyone stay at your home. AirBnB wouldn't last another day.
I agree that you shouldn't make judgements based upon only the profile picture. On the other hand, if they post things I find unattractive (like making fun of people of another race), I'm definitely not going to let them in my home. (OP seems to be a victim of the former and I sympathize with him)
Hotels have their place, but for extended vacations, having an entire home at your disposal can really change the quality of the vacation. More space to spread out and relax, a kitchen so you can cook some meals, etc.
But if you get it right, is there any legitimate explanation for why statistical differences would exist? Or do you baseline against the entire AirBNB population (which may be biased in of itself)?