Updated November 12, 2020
The federal government does not provide any protection against discrimination in rental housing based on sexual orientation or gender identity. However, if you live in one of the states that prohibit discrimination on the basis of sexual orientation in businesses that serve the public (see Nolo's article Healthcare Antidiscrimination Laws for Gays and Lesbians), a landlord may not refuse to rent to you because you are lesbian or gay. Likewise, landlords in these states cannot terminate a lease or end a month-to-month tenancy because of your sexual orientation. Some of these states also include transgender status in the class of people protected from discrimination. And some cities offer protections too.
If your state does not have antidiscrimination laws protecting you, then your landlord can legally refuse to rent to you because of your sexual orientation. However, your landlord probably can't terminate your lease early unless you've violated a lease clause. You won't get much protection in a month-to-month tenancy though, unless you live in a rent controlled area, which might make it harder for the landlord to terminate the tenancy. To learn more about the law in various states, see Nolo's article Tenant Rights Against Sexual Orientation Discrimination.
Sexual orientation discrimination includes being treated differently or harassed because of your real or perceived sexual orientation—whether gay, lesbian, bisexual, or heterosexual. This type of discrimination has been illegal ever since the Supreme Court's 2020 ruling in Bostock v. Clayton County that outlawed workplace discrimination based on sexual orientation. Prior to that ruling, about half of the states and the District of Columbia prohibited sexual orientation discrimination in both public and private jobs.
For additional information on laws affecting LGBTQ couples, see A Legal Guide for Lesbian & Gay Couples by Frederick Hertz and Emily Doskow (Nolo).
Antidiscrimination laws in about 22 states specifically prohibit doctors, hospitals, and medical facilities from refusing to treat people just because of sexual orientation. About 14 of those states also prohibit medical providers from discriminating based on gender identity.
Citing religious beliefs, some doctors and clinics in these states have refused treatment to LGBTQ people despite the laws requiring that they provide treatment. However, none of the state antidiscrimination laws recognize an exception for religious beliefs. In a recent case, the Supreme Court of California unanimously ruled that medical clinics must comply with California's antidiscrimination laws, regardless of the religious beliefs of those working in the clinic (the case is called Benitez v. North Coast Women's Care Medical Group). To learn more, and for a list of states with antidiscrimination laws, see Nolo's article Healthcare Antidiscrimination Laws for Gays and Lesbians.