Off-topic: I've read philosophy paper/essay things which use the genderless pronouns 'ey', 'em' and 'eir'. I would use those because I find assigning a gender awkward and the singular 'they' is wrong, but I worry about looking like a loser. Finland is so progressive.
But singular they is
NOT wrong. It has been used throughout modern English and nobody is confused when they see it.
The word "they" can be used to indicate uncertainty of gender, number or identity. It can also be used when the antecedent is known to be plural. At some point (probably right after denouncing split infinitives and terminal pronouns, both of which are perfectly acceptable) someone declared by fiat that the first usage was verboten.
They then went on to presumably read that "All men are created equal" and decided that women are neither created nor equal, and therefore not worth mentioning at all. Sooner or later, women decided that that attitude was not to blithely be put up with.
You will notice that nowhere in the preceding two paragraphs do the words "he," "him," "his," "she," "her" or "hers" appear. But I am not forced to conjure ad hoc substitutes to make my point clear; singular they works perfectly well to achieve this. The goal of written communication should be to convey the relevant ideas. When following a "rule" makes that goal easier, it should be followed, but if following such a "rule" interferes with communication, it should be immediately abandoned without a second thought.