Once you use a listing service that opens it to the public then there are all sorts of rules and laws that follow.
Why? You just state that like it's an obvious fact, but compared to "the sky is blue" it does not immediately follow.
Want to keep your rules? Don't use a listing service.
Why? That I need to follow the rules of the listing service, fine. That's part of signing the EULA when you register with it. But why do these rules have to be/contain specific rules? Why can the listing service not make up whatever rules it wants? It doesn't follow.
Rent to whomever you want, but don't advertise it to people you have no intention of renting to. That is what is illegal.
Ok, so add a filter to the listing service that allows the landlord to say "no men and no asian people" if they want, or "only single mothers of african decent" if that's their preference. What's wrong with that? If you find that nobody wants to rent to group X - go and figure out what's the reason for that and put your energy into fixing that. At the same time, there's suddenly a business opportunity for people to rent specifically to that group. The more they are discriminated against, the less competition and the more interesting it is to rent specifically to them.
Suppressing prejudices doesn't work. They don't go away just because you can't say it. Addressing them in an intelligent way is a much better approach.