That's not true at all.
You can't advertise that you discriminate but you generally can discriminate if (1) it's fewer than 4 units and the owner lives on premises, (2) it's a single family home owned by a person and rented w/o a broker, or (3) various other exceptions like religious organizations.
I suspect legally most airbnb landlords are in the clear.
I'm not a lawyer, but I do manage an apartment building. We don't discriminate; we just rent to the applications with the highest income and credit ratings.
I also suspect it would be in AirBnB's interest to weed this out, but since as a company they have no ethics, nothing will happen until there's a super embarrassing incident and it becomes news. eg Beyonce gets screwed by AirBnB and tweets it.