Airbnb can do whatever they want in property they own/lease. However since they 'share' (funny word that) people's private homes they will have to live with the fact that those people will refuse guests for whatever reasons they feel like, this is the flip side of the coin of not having a relationship where they are in control (employer, employee, owner of the premises). Airbnb wants to have its cake and eat it too,…
If Airbnb were a local chamber of commerce making bookings for bed and breakfast places, it might be valid that they're just a booking office.
But they're a major source of accommodations in large cities. As such they have to at least pretend to abide by those cities' antidiscrimination regulations. This policy is a way to do that without customizing the rules for each jurisdiction.
People are free to use less controversial ways to offer their property for short term rent. I do that, and not because I discriminate (I don't), but because I want to keep a little bit more wealth in my community rather than sending it all to Sand Hill Road.