In fact, grammar is only a description of the language. A man-made description of the language. Some people do research into that description, (a slippery subject to observe) and,  like in Science, it sometimes takes a long time for the results of the research to get into the textbooks. In this case, that means a new description of the language i.e. (shock and horror) a new grammar rule.

And that is apparently is the case here for the “gender-neutral pronoun“

What is a gender-neutral pronoun,  and why do we need one?

“If the person from the hotel rings, tell him we need two double rooms”

- but there’s a good chance that the “person” from the hotel is a woman.

“Yes, but the rule says that male form (him) in all inclusive, and covers women too” I hear you say.

So you mean like in mankind, chairman, etc..

Here’s what the people at Coe College, Iowa, USA tell their students about these kinds of words

“(…) Yet because the idea of sexism is relatively new, and because different groups have reached different stages of resentment against sex-weighted language, it is not easy to say how far you should go toward purging English of its longstanding favoritism to the male. The title Ms., which does not indicate marital status, is becoming well established as the female counterpart to Mr., and you cannot go wrong by changing stewardess to flight attendant and cleaning lady to housekeeper. Actress and waitress, on the other hand, have so far resisted all pressure to step aside for genderless words; if you used actor and waiter to indicate women, readers would be misled or taken aback. Are mankind, man-made and chairman offensive? More and more readers believe they are. You can substitute humanity for mankind and artificial for man-made, without attracting notice; but chairperson, though it is rapidly becoming common, will still bother some readers. Many people find person-suffixed words clumsy and self-conscious. Before using one, try finding a neutral alternative: not congressperson but representative, not policeperson but officer.”

ref.

In the same way, the  sexist him-as-all-inclusive, has actually faded from the language and the form which is used nowadays is “them” – as a singular pronoun.

“If the person from the hotel calls, tell them we need two double rooms.”

People who worship the Grammar God will insist that “them” is inappropriate here, because it is a plural form being applied to a single person. But they are just ignoring the fact that people have used it for a long time now in constructions like this. Be careful though, it can’t be used in specific cases such as, “If you see Jonathan, tell them to come back at five.“

Basically the rule is, if you know the gender, use it (If you see Jonathan, tell him to come back at five), and if you don’t know the gender, use “them/their even for the singular.