In California (the rules on this vary considerably by jurisdiction within the US), there is generally very little limit on discrimination by those renting out a room to a single roomer/boarder (but not if they are renting to multiple roomers/boarders), in an owner-occupied single family dwelling, though they generally can't advertise preference on any protected axis except gender, and only for that when there are shared living areas.
In a case like this, renting out the entire place when the terms of the rental is that the owner won't be there, this exception wouldn't seem to apply, though Idaho may have different rules (I'm having more trouble quickly finding a good description of Idaho's rules.)
Good luck, there's not much for rental regulations in the state of Idaho, and literally nothing for short-term rentals. It would come down to whether renting a property on AirBnB constitutes a lessor/lessee relationship, in which case the Fair Housing Act automatically kicks in.
Good thing this home is in Idaho...
Serious (offtopic) metaquestion: why is the postmodern view that all people, including violent criminals, are victims/products of their environment, but racists are uniquely and irredeemably evil to their core?
Usually it's more about a form of unstable and contextual xenophobia.
But it's not just against people. Also about all living things, object, behavior, events...
People are label racists like it's a deep nature, while it's most likely a small symptom of poor education + a twisted defensive reaction that is bigger than that, and is not particularly linked to race.
Well, I don't agree that that is the postmodern view, unless you define "postmodern" to specifically mean that view so that it is tautologically true; particularly, I don't believe that its all that common for any person (regardless of whether the label "postmodern" applies) to hold simultaneously to both of those beliefs. They may both be beliefs that are visible in some segment of the population, and there may be some overlap, but I don't think there is much correlation.
But, in any case, even if they were commonly held together, there is nothing inconsistent in believing that all beliefs and behavior patterns are products of the interaction of the individual with the external environment, and believing that there are certain beliefs and behavior patterns that, once established, are not correctable through any change in the environment that other people can effect (even if the same behaviors/beliefs may be made less likely to manifest in those who have not already manifested them), such that those behaviors/beliefs only go away when the people holding them die.
Hence why we don't expect to successfully re-educate them, and will have to outlive them instead.
But I suspect that the nature of postmodernism means we won't really be able to resolve what views are and aren't consistent with it to any objectively satisfying degree ;-)
Of course, discriminating in this way is already illegal for normal rentals, but when you have rentals of rooms in people's houses I believe it actually is legal for hosts to discriminate in some cases.
I really can't see how any sort of effective enforcement method could exist other than waiting for the racist assholes to die, sadly.