I think it really depends on what type of property is being rented out, and whether it's a full unit or a room.
Furthermore, landlords don't choose purely on race. They also select based on the tenant's profession, or whether they are family members or friends.
Also, both landlords and tenants have the right to be as picky as they want. Tenants also actively choose landlords.
The truth is, there are many other factors that make a deal. Let's not make this about race please.
(I know this as I also recently rented a unit, and if you are curious, no, I didn't rent from a landlord that's my race profile)