Why don't we consult the experts on usage? Here's what the Chicago Manual of Style says on the matter:
5.48: Singular “they”
Normally, a singular antecedent requires a singular pronoun. But because he is no longer universally accepted as a generic pronoun referring to a person of unspecified gender, people commonly (in speech and in informal writing) substitute the third-person-plural pronouns they, them, their, and themselves (or the nonstandard singular themself). While this usage is accepted in those spheres, it is only lately showing signs of gaining acceptance in formal writing (see 5.256), where Chicago recommends avoiding its use (see 5.255). When referring specifically to a person who does not identify with a gender-specific pronoun, however, they and its forms are often preferred. (They used in this sense was the American Dialect Society’s Word of the Year for 2015.) Like singular you, singular they takes a plural verb. So when the context requires it, they/them/their/theirs, like you/your/yours (long used as both singular and plural forms), can be used to refer to one person {they have a degree in molecular biology} {their favorite color is blue}. And themself (like yourself) may be used to signal the singular antecedent (though some people will prefer themselves) {they blamed themself [or themselves]}. A number of other gender-neutral singular pronouns are in use, invented for that purpose; forms of these are usually singular and take singular verbs. In general, a person’s stated preference for a specific pronoun should be respected. See also 5.251–60.