What the Catechism has to say.
2357 Homosexuality refers to relations between men or between women who experience an exclusive or predominant sexual attraction toward persons of the same sex. It has taken a great variety of forms through the centuries and in different cultures. Its psychological genesis remains largely unexplained. Basing itself on Sacred Scripture, which presents homosexual acts as acts of grave depravity,
141 tradition has always declared that “homosexual acts are intrinsically disordered.”
142 They are contrary to the natural law. They close the sexual act to the gift of life. They do not proceed from a genuine affective and sexual complementarity. Under no circumstances can they be approved.
2358 The number of men and women who have deep-seated homosexual tendencies is not negligible. This inclination, which is objectively disordered, constitutes for most of them a trial. They must be accepted with respect, compassion, and sensitivity. Every sign of unjust discrimination in their regard should be avoided. These persons are called to fulfill God’s will in their lives and, if they are Christians, to unite to the sacrifice of the Lord’s Cross the difficulties they may encounter from their condition.
All emphasis is mine.
Arguably, refusing to rent to the them may be considered “unjust” discrimination. A look back at my posting history will tell you that I am unutterably opposed to homosexual activity. However, the dignity of the individual persons is the questions here.
Other posters have compared this to renting to abortionists or unmarried heterosexual couples. While useful, I think the comparison to a heterosexual co-habitation falls a bit short as that is (probably) not a disordered activity. The abortionist comparison is also different as that is an opinion held by someone, rather than a “lifestyle”.
Another poster derided you by saying it was not any of your business. That is also incorrect because as a landlord, you do have a certain, albeit minimal, responsibility for both your tenants. You would not want a disruptive renter, for example.
While a difficult issue, I personally think the choice should be up to you as to whom you rent to. For example, if you only wanted to rent to people with no children, you should be able to. Likewise, if you only wanted to refuse to rent to unmarried heterosexual couples, you should be able to. Unfortunately that is no longer permitted as a result of federal court rulings.
Laws are being changed and courts are ruling resulting in special rights are being given to people who
choose to engage in homosexual behavior. (Important!
behavior, even sexual, is always a choice! Do not put words in to my mouth!) You may have no legal recourse if you choose not to rent to these people.