It's perfectly standard. You're probably already accustomed to using it for a person whose identity you don't know, unless you walk around saying things like "I hope this person comes back to get his or her umbrella."
Even if you know what gender the person is it's not uncommon to use they
"Well officer, I saw them walk from their car up to the door then they turned and looked around, that's when I saw them pull the ski mask down, draw their gun and enter the bank"
---
Manager: What was the customer doing when you told them to leave?
Clerk: Well I had been trying to help them with their project but they kept stepping into my personal space, then he places his hand on me and that's when I decided they'd crossed a line and needed to leave
---
Most people wouldn't even bat an eye swapping they out for he/she in conversation in person.
It would depend on context, if you ask me. The bank robbery was across the street & half a block down? Completely unremarkable to say "they". The clerk is complaining about sexual harassment, hand on thigh? Avoiding "he" implies a careful choice not to say, either to hide an identity, or because the customer was obviously confusingly gender-ambiguous.
I interpreted “they” in the second one as implying distance from the person in question, like the speaker wants nothing to do with them and is emphasising that they were a stranger. Possibly part of why saying “they” feels uncomfortable to people, but I’d never realised it until reading that example.
In my case if I don't know someone well, or at all, without thought I use gender-neutral terminology they/them/their and with pets and babies, again without thought, I naturally use it.
"Well officer, I saw them walk from their car up to the door then they turned and looked around, that's when I saw them pull the ski mask down, draw their gun and enter the bank"
---
Manager: What was the customer doing when you told them to leave?
Clerk: Well I had been trying to help them with their project but they kept stepping into my personal space, then he places his hand on me and that's when I decided they'd crossed a line and needed to leave
---
Most people wouldn't even bat an eye swapping they out for he/she in conversation in person.