Do you think “their” should be acceptable as a nongendered singular pronoun?
I wouldn’t do it, but my neighbor can make up their own mind. 10.8%
Depending on how you look at it, this is either one of the most frequent blunders in modern writing or a godsend that allows us to avoid sexism.
—Bryan A. Garner
Garner goes on to say: “Where noun-pronoun disagreement can be avoided, avoid it. Where it can’t be avoided, resort to it cautiously because some people may doubt your literacy …”
See also: John McIntyre’s list of zombie rules (last item, so presumably the least breakable). There are three categories for zombie rules. The first is for those that are “fully exploded,” the second for those “not dead yet.” Think of the third as for the ones that can still hurt you; approach with caution.