If you'd like to target a specific demographic you can do so using either inclusionary or exclusionary targeting. Only one of those systems also allows you to explicitly exclude one or more groups rather than just target a subset of groups. Your example seems to be a very charitable interpretation of how exclusionary targeting could be used. There's (probably) nothing wrong with it if it's used that way. But you could just as easily use the system you described to prevent a variety of protected demographics from being able to see the advertisement whatsoever.
https://www.ajc.com/visitor_agreement_mobile_old/
Equal Housing Opportunity. Any real estate advertising on this website is subject to the Fair Housing Act, which makes it illegal to advertise "any preference limitation or discrimination based on race, color, religion, sex, handicap, familial status or national origin, or an intention to make any such preference, limitation or discrimination." Georgia state law also forbids discrimination based on these factors, except that it forbids discrimination based on "disability" rather than "handicap." Familial status includes children under the age of 18 living with parents or legal custodians; pregnant women and people securing custody of children under 18. To complain of discrimination call the U.S. Department of Housing and Urban Development at 800-669-9777.
https://www.sharinghousing.com/what-the-fair-housing-act-mea...
Craigslist says something different.
https://www.craigslist.org/about/FHA#roommates
Under federal Fair Housing law, the prohibition on discriminatory advertisements applies to all situations except the following:
Shared Housing Exemption -- If you are advertising a shared housing unit, in which tenants will be sharing a bathroom, kitchen, or other common area, you may express a preference based upon sex only.
Private Club and Religious Exemptions -- A religious community or private club whose membership is not restricted based upon race, color, or national origin may restrict tenancy only to its members in a property that it owns, and may advertise to that effect.
Housing for Older Persons Exemption -- As discussed below, certain complexes for elderly persons are exempt from prohibitions on familial status discrimination, including the prohibitions on discriminatory advertising.
>Decision-making: Although the prohibition on discriminatory advertising applies to roommate and shared housing situations, federal Fair Housing laws do not cover the basis of decisions made by landowners who own less than four units, and live in one of the units. This means that in a situation in which a landlord owns less than four rental units, and lives in one of the units, it is legal for the owner to discriminate in the selection process based on the aforementioned categories, but it is illegal for that owner to advertise or otherwise make a statement expressing that discriminatory preference.
I wonder if someone who has a particular dietary restriction (kosher, halal, gluten free, vegan, etc.) can express a preference for a like minded person.
I also told the recruiter that I wasn’t going to hire a guy because he smelled like cigarette smoke, I would be working closely with him and it bothered my asthma. Cigarette smoking is not protected in some states - including mine.
So if you're the Catholic Church running a women's boarding house on the upper east side of Manhattan, you are allowed to advertise to (and rent to) only women, but you can't restrict it further to only Catholic women.
Speaking of which, the Roomi app might potentially be doing illegal things in turning housing search into a social network.