Singular they, or the use of the pronoun they to refer to one person, has been around for centuries. Both Chaucer and Shakespeare used it. It’s in the King James Bible. But since the early days of English grammar textbooks in the 19th century, it has been considered a mistake. For over 100 years, students have been urged to re-write sentences like “Everyone has their own ideas” with a singular pronoun: “Everyone has his own ideas.”
The problem with that fix is that it necessitates a decision on gender. What if you don’t have a specific person in mind? What if you don’t know the gender of the person you’re talking about? What if the person doesn't prefer a specific gender? The solution to that problem was for a long time the clunky “Everyone has his or her own ideas,” or changing the subject to a plural, as in “People have their own ideas.” In regular speech and informal writing, the singular they rolled on, becoming common enough that even the sharpest-eyed editors sometimes failed to catch it before print.
In 2015, The Washington Post became the first major publication to drop the prohibition on singular they from its official style guide. Now the Associated Press has done the same, albeit “in limited cases … when alternative wording is overly awkward or clumsy.”
While the "Everyone has their own ideas" sort of singular they is commonly used for reference to a non-specific person of unknown gender, the AP guide also deals with the use of they as a pronoun for a specific person who chooses not to identify as male or female. In that case, the direction is to “use the person’s name in place of a pronoun, or otherwise reword the sentence, whenever possible. If they/them/their use is essential, explain in the text that the person prefers a gender-neutral pronoun.”
As always, “clarity is a top priority.” That’s the most important rule for any good style guide and for any good writing. A change to a style guide isn’t a change to the language, but a relaxing of a restriction in places that made clarity a little harder to achieve.