Housing law has special sets of protection distinct from even the law governing general public accommodations, so (without an argument that the specific service is be very much like housing), it's probably not the most reasonable analogy to use.

This depends on the terms of the lease. That seems completely non-controversial to me. There's a bunch of stuff in my lease that I couldn't do, which are perfectly legal in many other contexts (smoke inside, have a dog, have big parties, etc...). Likewise, a KKK friendly lease would also be legal and honestly I don't think you'd have a hard time finding people who would be willing to have you.

And I've yet to find someone who has said they can't discuss their beliefs. They just don't get "our" support to do it.