The title sort of says it all. I was using a roommate finding/room rental app when I noticed it had an option to filter for 'LGBT housing'. The Fair Housing Act forbids discriminating against sex, including sexuality. Thus I'm wondering how allowing preferential treatment to LBGT sexualities/genders wouldn't constitute discrimination?
The words of the prohibition in 24 CFR 100.60(a)are that
It shall be unlawful for a person to refuse to sell or rent a dwelling to a person who has made a bona fide offer, because of race, color, religion, sex, familial status, or national origin or to refuse to negotiate with a person for the sale or rental of a dwelling because of race, color, religion, sex, familial status, or national origin, or to discriminate against any person in the sale or rental of a dwelling because of handicap.
It would be discriminatory for the landlord to refuse to rent to a person because they are or are not of some sex. Based just on the plain language of the prohibition, the author of the app or operator of a website is not renting / refusing to rent. Nevertheless, Roommate.com was sued, and found not liable, though not on the grounds that they hadn't discriminated
Fair Housing Councils v. Rommate.com addressed an attempt to punish roommate.com on discriminatory grounds. The court states that "The pivotal question is whether the FHA applies to roommates". The court's reasoning is a clear application of the notion of "Congressional intent". As they say,
There’s no indication that Congress intended to interfere with personal relationships inside the home. Congress wanted to address the problem of landlords discriminating in the sale and rental of housing, which deprived protected classes of housing opportunities. But a business transaction between a tenant and landlord is quite different from an arrangement between two people sharing the same living space. We seriously doubt Congress meant the FHA to apply to the latter. Consider, for example, the FHA’s prohibition against sex discrimination. Could Congress, in the 1960s, really have meant that women must accept men as roommates? Telling women they may not lawfully exclude men from the list of acceptable roommates would be controversial today; it would have been scandalous in the 1960s
The court continued on other grounds, observing that
given that the FHA is a remedial statute that we construe broadly... we turn to constitutional concerns, which provide strong countervailing considerations
That is, even if you ignore congressional intent, there is a constitutional reason why FHA cannot apply to roommate choice.
SCOTUS in Bd. of Dirs. of Rotary Int’l v. Rotary Club of Duarte, 481 U.S. 537 stated that "the freedom to enter into and carry on certain intimate or private relationships is a fundamental element of liberty protected by the Bill of Rights", and "Courts have extended the right of intimate association to marriage, child bearing, child rearing and cohabitation with relatives". Then in order to "determine whether a particular relationship is protected by the right to intimate association we look to 'size, purpose, selectivity, and whether others are excluded from critical aspects of the relationship'". After extensive analysis centered around the point that "Government regulation of an individual’s ability to pick a roommate thus intrudes into the home, which 'is entitled to special protection as the center of the private lives of our people'", the court "adopt[s] the narrower construction that excludes roommate selection from the reach of the FHA".
TL;DR the FHA doesn't apply to roommates and it's legal to select one's roommates based on their race, color, religion, sex, sexuality, etc...
Whether this is lawful, has already been answered. Whether this is ethical (and by extension should be lawful) can be argued. Without knowing the intentions of the advertisers, your best approach would be to interpret this as a way to search for homes that are friendly towards queer folks. Similarly, tenants may be looking for homes friendly to their religion or race, neurodiversity, or hobbies. This filter lets advertisers be proactive and explicit about non-tangible aspects of the home.