You argue thus:
“If renting to a homosexual makes you complicit in his homosexuality, then renting to a thief makes you complicit in his theft, and renting to a liar makes you complicit in his lying, etc.”
Well, this is an inherently false syllogism. Renting to a thief does not make the landlord complicit in the theft, but if the landlord rents the house knowing that his house would be used by the unrepentant thief as a launching pad for a nearby heist the following morning, yes he is complicit. Indeed, in the secular word, this would be seen as a form of aiding and abetting the purported heist.
If knowingly renting to a father and daughter in an incestuous relationship to continue their incest is a sin (and also a crime) why should it be any different to those engaged in acts that are just as abominable to those in a homosexual relationship as do lesbians which is a sin (and was a crime in many states until a liberal supreme Court struck down such laws as unconstitutional) .
I don’t think appeals to “kindness” is of any help here either morally in the secular sense or spiritually in the biblical context.
What you say makes good sense. But then what of Jesus honoring the thieving, traitorous Zachias by dining in his home? Many people were as appalled by that as you might be by someone renting a room to a gay couple.