In any case, my mention of Shakespeare was an aside and not crucial to the overall argument of my post; so it is arguably you who are missing the point.
That's probably because most people don't refer to people as "they" except when specifically asked to. If people went around using "they" as the standard pronoun when referring to known people, there would be much more offense.
By the way, I am totally fine with not using singular they to refer to people who are genuinely offended by it. I just have not actually encountered any such person outside the class of 'argumentative people on the internet'. For this reason I think that 'use singular they if unsure' is good, though not infallible, advice.
Referring to someone as a "they" would be considered misgendering to a lot of people. It is not "not making reference to their gender" because the vast majority of people who want to be referred to as "they" are not cisgender. Referring to someone in this way suggests that you think they are not cisgender.
> I just have not actually encountered any such person outside the class of 'argumentative people on the internet'.
The neighbor who approached me after having been referred to as "they" was not an argumentative person on the internet. She was someone (who lives in a very liberal area, BTW) who was perplexed and offended to have been referred to that way.
For this reason I think that people who are offended by being referred to by 'they' are wrong to be offended. I think they're wrong in a way that, say, a trans woman is not wrong to be offended if someone insists on using 'he'. In the former case, the person may feel that they are being misgendered – but only on the basis of a dodgy linguistic analysis. Of course, we should accommodate people's pronoun preferences, regardless of whether we agree with their underlying logic in any given case.
The story about your neighbor doesn't really make sense to me. Surely it occurred to her that the other forum poster might not have cared much what her gender was, or have paid much attention to her photo, or simply didn't care to take a guess even if she appeared clearly female. To interpret this as intentional misgendering seems a bit nuts. If she was simply worried about whether she appeared clearly feminine in the photo, then that's an understandable anxiety, but one that has little to do with singular they. (If singular they were off limits then I guess the poster might have used 'he' instead, which hardly seems better.)
My understanding is that these days, we are not allowed to opine on whether others are wrong to feel offended. In modern parlance, I'd say that you don't understand why they're offended. It seems you're trying very hard not to, considering that this term is not the preferred term of reference for practically anyone who is cisgender.
If the best you can do is tell me that I have to accede to the ineffable and indefinite reasons for your neighbor taking offense, then I suppose the discussion is over. (Of course I do accede in practice - I’m not going to refer to her as ‘they’ just to be a dick.)
If you really believe that people are entitled to be arbitrarily offended by pronouns, then you can have no objection to trans or non-binary people being arbitrarily fussy about their use. I mean, I’m “woke” by HN standards and am all in favor of respecting people’s pronoun preferences. But even I don’t believe that the subject is entirely in the realm of subjective feelings of offense and beyond rational discourse.
> could also be offended to be referred to as "they" because it could imply that the person is in-between
‘They’ is gender neutral; its use implies nothing about a person’s gender. If someone gets offended anyway then the simplest solution is obvious - use their preferred pronoun. But taking offense at singular they doesn’t seem to be something common, at least in my experience. It’s certainly the option that’s least likely to cause serious offense if you can’t remember (or were never told) a person’s preferred pronouns, with at least as much cause.
I’d also repeat the following point. If we’re ok with cis people being fussy about being referred to using singular they, then presumably we must also allow trans or non-binary people to be fussy about their preferred pronouns. You can hold that the use of singular they to refer to known male or female persons is potentially objectionable; but then you should also recognize that other sorts of people might be similarly picky about their pronouns.
> [older people] may be confused
Confused != offended. But singular they has such a long history that I think such confusion is rather unlikely in practice.