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.