>If you spend a lot of time writing copy for the web or answering support emails, you know what I’m talking about. When you start a sentence, you can feel the nausea coming on from a mile away: there’s no gender neutral third person singular pronoun.

Technically, there is such a thing. "it" is a gender neutral third person singular pronoun[1] and even more amusingly it is not part of the proposed "replacement" list. It does sound very weird in most cases - and would definitely look dehumanizing in a support reply, but technically speaking the language is not broken.

[1]http://en.wikipedia.org/wiki/It_%28pronoun%29 . Example given: "Is it a boy or a girl?"