I don't know if this is really a tractable problem. At the end of the day, either airbnb lets hosts decide who stays or doesn't. If they don't let hosts decide, they'll likely lose a ton of hosts, since having someone stay in your home is a very personal thing and a huge risk. If they do, then they're going to have significant discrimination problems as long as people are discriminatory, i.e., basically forever.
I can think of one way AirBNB could attempt to persuade hosts: publish data showing that there is no correlation between any of [race, religion, national origin, disability, sex, gender identity, sexual orientation, age] and the likelihood of a guest being a poor guest (ending in an insurance claim, or maybe just a very bad review). If the data shows that there is no correlation, they can prove hosts have no reason t…
... Right.
Also, note that health insurer discrimination is the exception, rather then the norm (And it surprises me that it is even legal).