dennisgorelik is correct, and you are wrong, as to a specific scenario which I would still consider to be a "housing transaction". It is 100% legal to discriminate on the basis of race, sex, or any other characteristic at all when choosing a roommate (a special form of renting out your property). It is 100% illegal to place advertisements indicating that you will reject roommates based on race, sex, or other protected characteristic. So in that case, the law is very specifically about the contents of the advertisement, not about the behavior of discriminating against certain renters.
So are you saying it's not the spirit and letter of the Fair Housing Act to forbid discrimination? Or are you saying that HUD is not arguing that Facebook enables illegal discrimination on their platform?
Well, since housing discrimination is fully legal under some circumstances, I would indeed say that it is neither the spirit nor the letter of the Fair Housing Act to forbid discrimination. What is the alternative view?
