With its 18th edition, The Chicago Manual of Style has fully embraced the singular they.
This comes many years after the manual and the Associated Press mostly accepted the singular they in a development that one veteran editor called “the middle of the end for the insistence that ‘they’ can be only a plural pronoun.”
The new CMOS’s revised guidelines on pronouns can be found in the fifth chapter (Grammar and Usage). At 5.44 it is noted that “they can be singular as well as plural in sense” but is always paired with a plural verb even when referring to just one person. Write “they are happy” rather than “they is happy.”
The chapter later notes that the singular they is nowadays “used in reference to a nonbinary person” (i.e., a person who identifies as neither female nor male) in addition to the more traditional use when gender is unknown. “In recent years this usage has become accepted in more formal contexts … and Chicago now endorses it.”
I like that the guidance at 5.52 gives a nod to themself as an alternative to themselves when using the singular they: “And themself (like yourself) may be used to signal the singular antecedent when it appears to be the logical choice.”
Use of the singular they for those who identify as nonbinary is a matter of respect, as stated later at 5.52: “If an individual is known to use they and its forms as their personal pronouns rather than the gendered he or she, this usage should be respected.”
Later in the chapter, there’s a nine-item list of “options for gender neutrality” in pronoun use. The first suggestion is that in some cases a writer could omit the pronoun entirely.
“For instance, in the programmer should update the records when data is transferred to her by the head office, if there is only one programmer, the pronoun phrase to her can be omitted: the programmer should update the records when data is transferred by the head office. Note that the shorter sentence is tighter as well as gender-free.”