As anyone knows, referring in the third person about some one whose gender you do not know was a problem even in the days when gender was seen in purely binary terms. Repeatedly writing ‘he or she’ or ‘his or her’ gets tedious very quickly. The growing recognition and acceptance that gender was not binary but fluid initially seemed to compound the problem of the third person singular pronoun.

But as often happens, it is when a problem gets acute that people start looking for new ways to address it and the suggestion that rather than inventing a third term, we use ‘they’ in singular as well as plural form was an idea brilliant in its simplicity.

It was an idea I embraced immediately as soon as I heard about it. That is not to say that the transition was easy. I initially had twinges of unease whenever I used it in this new way because, being an old fogey, deliberately using this word in what would formerly have been considered an ungrammatical way was uncomfortable. But now I am so used to doing it that I don’t even think twice, though I have had colleagues who disagree with me and still frown on what they consider to be ‘wrong’ speech.

It appears that Merriam-Webster has given its seal of approval to this use.

3—used with an indefinite third person singular antecedent
//No one has to go if they don’t want to.
//Everyone knew where they stood …
— E. L. Doctorow

4—used to refer to a single person whose gender identity is nonbinary (see NONBINARY sense c)
//I knew certain things about … the person I was interviewing.… They had adopted their gender-neutral name a few years ago, when they began to consciously identify as nonbinary — that is, neither male nor female. They were in their late 20s, working as an event planner, applying to graduate school.
— Amy Harmon

Actually, as the dictionary points out, the third singular ‘they’ actually has a long history and has been used by eminent writers who probably wanted to avoid the circumlocution required to be obedient to the extant grammatical rules.

They, their, them, themselves: English lacks a common-gender third person singular pronoun that can be used to refer to indefinite pronouns (such as everyone, anyone, someone). Writers and speakers have supplied this lack by using the plural pronouns. // and every one to rest themselves betake// — William Shakespeare //I would have everybody marry if they can do it properly// — Jane Austen // it is too hideous for anyone in their senses to buy// — W. H. Auden The plural pronouns have also been put to use as pronouns of indefinite number to refer to singular nouns that stand for many persons. //’tis meet that some more audience than a mother, since nature makes them partial, should o’erhear the speech// — William Shakespeare // a person can’t help their birth// — W. M. Thackeray //no man goes to battle to be killed. — But they do get killed// — G. B. Shaw The use of they, their, them, and themselves as pronouns of indefinite gender and indefinite number is well established in speech and writing, even in literary and formal contexts. In recent years, these pronouns have also been adopted by individuals whose gender identity is nonbinary, as illustrated in sense 4 above.

An interesting example of how the rules of grammar are not set in stone but evolve under changing circumstances.