They, them and their have been used in the singular for quite some time.
I guarantee every one of you have used them so.
Not only have we always had gender neutral pronouns but once it was acceptable to use "he" as a gender neutral pronoun and Shakespeare famously said "everyone has their failings" and so called grammatical experts were not pleased. But early feminists were extremelynot pleased for a male pronoun to be considered gender neutral and were not pleased that they could be referred to as "he" yet excluded from many organisations as "women".
They and them has also been used in the singular, well, since before all of us were born. When we do not know the gender of the other person. Examples:
"They cut me up!"
"They sent me an email"
"I asked them what they thought"
Dear readers, we are on an anonymous forum, we do not know who we are talking to. We would easily use they or them in the singular, for example:
Poster 1 "Has anyone seen username? I haven't seen them post for a week"
Poster 2 "yes they were posting this morning"
Poster 1 "were they? Oh I was worried about them"
As the language evolves people are trying out more pronouns, some will probably come into regular use and some won't.
Due to the need for gender neutral pronouns and their use in language, lots of people regularly use they, them or their in singular even when they know the gender of the person they are referring too. As you can probably tell, I am one of those people and despite using both words in the singular here on gransnet even when I know th gender, not a single pedant has pulled me up... because they also do it without realising.
If you are asked to use a pronoun I would oblige as its polite. If you aren't sure of a pronoun, using they, them or their is perfectly acceptable and long understood in the English language (even though people don't seem to notice they are already doing it).
If you are struggling remember those early feminists fighting to bring more pronouns into use and thankfully winning.