I see what you mean, but I think it's slightly the wrong analysis on a linguistic level. 'They' doesn't generally introduce a presupposition of non-binarity (either semantically or via pragmatic inference). If it did, it would be hard to account for the innumerable examples of 'they' being used with unambiguously masculine and feminine quantificational antecedents.
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.)