Long before the use of generic he was condemned as sexist, the pronouns they, their, and them were used in educated speech and in all but the most formal writing to refer to singular indefinite pronouns or singular nouns of general personal reference (which are often not felt to be exclusively singular): If anyone calls, tell them I'll be back soon. A parent should read to their child. Such use is not a recent development, nor is it a mark of ignorance. Shakespeare, Swift, Shelley, Scott, and Dickens, as well as many other English and American writers, have used they and its related case forms to refer to singular antecedents. Already widespread in the language (though still rejected as ungrammatical by some), this use of they, their, and them is increasing in all but the most conservatively edited American English. This increased use is at least partly impelled by the desire to avoid generic he or the awkward he/she and he or she when the antecedent’s gender is not known or when the referent is of mixed gender: The victim had money and jewelry taken from them. It’s hard to move an aging mother or father from their long-term home.
However, while use of they and its forms after singular indefinite pronouns or singular nouns of general personal reference or indefinite gender is common and generally acceptable, their use to refer to a single clearly specified, known, or named person is uncommon and likely to be noticed and criticized, as in this example: My hair stylist had their car stolen. Even so, use of they, their, and them is increasingly found in contexts where the antecedent is a gender-nonconforming individual or one who does not identify as male or female: Tyler indicated their preferences on their application.
And although they may be used as a singular pronoun, they still takes a plural verb, analogous to the use of "you are" to refer to one person: The student brought in a note to show why they were absent. See also he¹.