Having said that, the suggested gender neutral pronouns are ham fisted, but maybe you should be asking people what they want to be called, before you start calling them? It only takes a few seconds. I'm sure you can all spare it.
Having been subjected to something like this, tho not so hamfisted as this, when I was a TA back in grad school, the motivation to encourage the use of gender neutral language is not for when speaking to or of specific people. Not even the most ardent of gender neutral advocates would say something like "When Hillary Clinton was Secretary of State, zir worst mistake was using a private email server." Rather gender neutral language advocacy is about avoiding language like "I will be a swift witness against the wage earner in his wages." lest someone might get the impression that the speaker was referring to just male workers.
Save us from very long jokes with very bad punchlines. Ernesta