It’s completely natural too – completely ordinary, grammatical English. When a native speaker uses that construction, nobody blinks, because it feels perfectly correct.
The only people who would argue otherwise would probably be formal, prescriptive grammarians who take the position that grammar should dictate how language is spoken. Most people who study grammar are in the descriptivist camp, observing that grammar merely describes how people use language.
Prescriptivism isn’t really all that old as an idea. It goes back (in the English-speaking world anyway) only a couple hundred years at the most, and has its roots in classism. People of higher classes who had access to expensive education got the idea that dictating how people “should” speak would help identify “quality” people.
Linguists recognize that all languages change constantly and that formal grammar can only be used to observe and document those changes, and perhaps to help non-native speakers master their new tongue.
When people get all huffy about using they in the indefinite neutral-gender singular sense like you used above, they must resort to prescriptivist grammar arguments to make any kind of case. It’s funny to watch people do this who would never otherwise defend prescriptivism, which is highly out of favor in academia.
Things get a bit touchier when it comes to using they in the definite, singular neutral-gender sense to refer to a specific person. That really is new in the language, and doesn’t feel natural to most native speakers.
But it’s started to feel natural to me and lots of other folks, because practice makes perfect.
Languages are slippery critters, though. It can be very difficult to make a deliberate change to a language, because they’re organic things that react unpredictably to stimuli. But you know what? It looks like the definite neutral-gender singular they really has taken off. And that’s extremely cool, because it’s an extremely useful pronoun for tons of reasons.
I speak a couple languages that have had similar gender-neutral pronouns forever, and it feels weird that English hasn’t always had something so useful.
