I actually really like Stallman's comment on the subject:
"
Every language has grammar rules. They are in the minds of speakers of the language — including, for English, me. The fact that they weren't decided by an official edict doesn't mean these rules are a trivial matter; demanding people change their grammar rules is an affront. You might succeed in convincing me to change the English grammar rules in my mind, but don't you dare demand it. "
To more clearly answer your question -- it becomes correct when the corpus of the English speaking world decides it does. That hasn't happened since 1300, why would it happen today?
> You might succeed in convincing me to change the English grammar rules in my mind, but don't you dare demand it. "
Oh, the irony. The person writing a ruleset on grammar for others to follow feels uneasy when others ask the same of him. If he ever listens to hip-hop –or visits Australia– they's gonna have a meltdown.
Well there's also the difference between a native of the southern US and the northern US, the east and the west -- all are distinct dialects. I don't know how many US dialects there are, but I've been exposed to many of them.
Singular you was incorrect for centuries before it was correct. In between incorrect and correct, you have a good 100 years of grey area usage where social pressures urged change. This is no different.
The fact that a grammar change hasn't happened yet is no indication that it won't.
I asked for proof, not your personal anecdote. I too have lived in many cultures. Singular they has been commonly accepted everywhere that speaks English.
Think about the phrase "Everyone loves their mother". Everyone is a singular noun. According to you, this usage would be debated everywhere, because the "correct" English would dictate "Everyone loves his mother".
I dare you to find an English speaking country anywhere in the world where the majority thinks "Everyone loves his mother" sounds more correct. You won't. Because singular they has been a thing for centuries and is entirely common at this point.
The part where you're tripping up is how singular they is used. It is common everywhere in the world to use it in situations of ambiguous identity. The reason you find it absurd is that now we are using it in situations of specific identity but ambiguous gender. That form of usage is indeed new and not majority usage everywhere, but that still does not mean it is incorrect. Actual communication with people is what defines correctness is the English language.
[0]: https://en.wikipedia.org/wiki/Singular_they#Older_usage