And even if we remove all racial characteristics from the application, judging by socioeconomic status is defacto racial discrimination because of the correlation between status and race.
And even if there were no correlation between socioeconomic status and race, it still seems wrong to discriminate against a poor person even if, on average, poor people cause more problems for the landlord.
If you're "playing the odds" by using race as a proxy for socioeconomic status, then this is wrong. It's also a pretty poor proxy, in my experience. What about our judgements about people's judgements? (Meta-judgements.) If you're equating making a factual determination about socioeconomic status with racial discrimination, then you are using the same sort of statistical proxy you're arguing against!
And even if there were no correlation between socioeconomic status and race, it still seems wrong to discriminate against a poor person even if, on average, poor people cause more problems for the landlord.
Really, socioeconomic status is a proxy for behavior and ability to pay. Because of its rating system, AirBnB can function as a meritocracy. The fact that it has an effective rating system is a competitive advantage. Provided they are not absolutely locked out, it seems feasible for a poor person to earn a good rating in such a meritocratic system.
If AirBnB wants to further social justice, then it should make the meritocracy of the ratings fairer, instead of denying its utility to hosts. The former increases justice. The latter is using market power to force hosts into behaving how you want. You don't win hearts and minds by forcing people to do things. You win them by facilitating their voluntary transactions with all different kinds of people. (I've seen this first hand. I saw one of my classmates go from being a homophobe to being the best friend of a gay activist, by bonding over soap operas.)
The majority of recent uses of the term "white supremacist" make me cringe. It's mostly propaganda: A deliberate emotional attack often based on a false equivalence. In any case, the impression I have as a frequent AirBnB user is that most AirBnB owners aren't interested in renting on the basis of "race, color, religion, sex, familial status, or national origin." Rather, they are most interested in education level, socioeconomic status, and manners as a proxy for risk. They just want to determine how likely the potential guests are to cause an out-sized expense in time, treasure, and emotional energy.
Not letting people exercise such judgement is effectively creating a privileged group on the basis of race, color, religion, sex, familial status, or national origin. (EDIT: However, I would only reserve such leeway for people renting out a part of their own residence. People who own or have leases on a large number of rooms/properties renting on AirBnB should have to abide by such laws, as they are basically in the hotel business, and are covered by the applicable laws. Also, their increased transaction volume makes such laws enforceable, whereas a genuine single family on AirBnB would often not have such volume. Equating these different classes of AirBnB user would be a False Equivalence.)