Many grammarians these days say it is OK. (Most of us are using it anyways, even unconsciously.) The Chicago Manual of Style and the Associated Press discourage it.
Others insist that the singular “they” is social justice for people who don’t identify as either male or female...and one’s opinion on the matter, like too many other social justice tropes, has become a tool to separate the woke from the worst.
But...we’re talking about two different issues here.
One is respecting someone’s requested personal pronouns. If a person wants to be called “they/them/their,” following that request is not being “politically correct.” It is simply good manners.
The other is using it in general writing. When creating newsletters for a client, I would proofread the Word doc sent to me and rewrite examples of the singular “they,” as follows:
[It] would be physically impossible for one person to have his or her [originally: their] finger near enough to the pulse of each and every market to do any good
[The] way average Americans [originally: the average American] can generate 20% to 30% returns on their investment
Sellers [originally: A seller] will never allow a loan to be tagged to their name for very long
Some people [originally: Someone] who buy [originally: buys] at the “right” time can see the value of their investments soar up to the sky
I could have just left those examples alone. But singular “they” in general writing irritates me to no end, like having a popcorn shell stuck between my teeth when I have no access to floss. I can’t pinpoint the exact reason why I feel that way. It could be because I like logic in my language (and everything else, for that matter).
Here’s a thought: you can respect singular “they” as an individual’s personal pronoun AND avoid it in your own writing as much as possible. “Every student must bring their own laptop” is all right in all but the most formal writing. But “All students must bring their own laptops” is equally as right.
Let this be your permission slip: You can use the singular “they”, or not, depending on how much it feels like stuck popcorn shells. It’s not that hard.