I don't think you're lying. I think you're unfamiliar with your native language. As a fellow native English speaker, singular they sounds perfectly natural to me and has appeared in a great deal of prose that I've read, and not just 21st century text.
Do you think the people who downvoted you are all non-native English speakers passing judgement on you?
Everything we as linguists can do is to say that x feels natural to this many people and unnatural to this many people. However, when writing something, if enough people think that something feels unnatural, maybe you should investigate if you can phrase things differently so that more people will accept it.
People feel what they feel and can't be wrong about what they feel (because it's feeling, not a rational thing).
I don't disagree with that in any way whatsoever. But it doesn't mean that the OP is fundamentally correct either. I find the phrase "he/she" to be awkward, ignoring whether it's inclusive or not (which it isn't). "He" is fundamentally gendered despite what many people want to believe and is even less inclusive (even if we assume only the male and female genders, it necessarily excludes half the population). Consequently, singular "they" ends up being the most natural way to express a non-gendered arbitrary person, especially given that English has an 800+ year tradition of using it in that sense.
That speaker has probably seen singular they countless times without raising an eyebrow, and probably used it themselves. They may report being uncomfortable with it when their attention is called to it, but that doesn't always reflect their actual usage.
You get a better understanding by analyzing a corpus than by asking people. And the corpus makes clear that a lot of people have been comfortable with singular they, for a long time. I've even seen examples of people decrying singular they in sentences using singular they.
The self-reports are also data that's informative to the linguist. But they need context to gain perspective, because they're not always identical to what the speaker generates or accepts.
For a start I find it telling that my comment was downvoted to -4 instantly. How can you downvote someone for stating what they do or don't find natural in their own language? Do you think I'm lying? Maybe I should start making comments about what I find natural in French instead?
You've all given examples of contexts where you don't find it unnatural. I agree with s some of them, so let me correct my original comment: it doesn't always sound natural.
> "I interviewed a developer yesterday." "Were they any good?"
This sounds OK if the gender has not yet been mentioned, but as soon as it has been mentioned it would be unnatural to use "they".
> Do they have grey hair? Yes, they do.
Also OK, until the gender has been established, as above.
> "Fin updated their profile picture"
This sounds completely unnatural to me and yes, I have noticed it. This is the same usage as in the PR in question here.
I also find it unnatural when "they" is used as the subject of a sentence in singular, like "When they travelled to London, they drank tea". If that's a single person, it sounds really jarring.
I think it's probably to do with the verb conjugation rather than the pronoun. As a French speaker you probably understand that the verb is equally, if not more, important than the pronoun. In Spanish they don't even bother with pronouns, it's all about about the verb. Unfortunately "they is" sounds totally wrong to every native speaker, so you're stuck with "they are", which is used for plural.