The question of whether or not to use “their” to replace the awkward “his or hers” has been the eye of a grammarian hurricane for some time now. I’ve found that this usage has been generally accepted, particularly in the latter half of the 1990s in the wake of efforts to reduce the level of sexism built in to traditional grammar constructions.
The New Fowler’s Modern English Usage (1996) has this to say about the history of the controversy around the word their:
Fowler (1926) was among those who objected to the use of their in contexts that call ‘logically’ for his (though this use of the masculine gender to cover both has lately been called into question) or his or her. The issue is unresolved, but it begins to look as if the use of an indefinite third person singular is now passing unnoticed by standard speakers (except those trained in traditional grammar) and is being left unaltered by copy editors.
Notably, this controversy does not apply to the word them:
As the OED says, it is ‘often used for “him or her”, referring to a singular person whose sex is not stated, or to anybody, nobody, somebody, whoever, etc.’. Example: Nobody else…has so little to plague them.—C. Yonge, 1853 (ibid.)
Some traditionalists, like Strunk & White, do not appreciate this change and strongly advocate the wholesale rewriting of passages which would historically have utilized “his” as a catch-all pronoun meant to signify all genders. In the Fourth Edition of “Elements of Style” (2000) S&W defend this tradition: “The use of he as a pronoun for embracing both genders is a simple, practical convention rooted in the beginnings of the English language.” However, even they state:
“Substituting he or she in its place is the logical thing to do if it works. But it often doesn’t work, if only because repetition makes it sound boring or silly.”
What’s interesting to me is that the most traditional usage of “they” was as a singular pronoun in the first place:
“He” started to be used as a generic pronoun by grammarians who were trying to change a long-established tradition of using they as a singular pronoun. In 1850 an Act of Parliament gave official sanction to the recently invented concept of the “generic” he. In the language used in acts of Parliament, the new law said, “words importing the masculine gender shall be deemed and taken to include females.” – Excerpted from article by Carolyn Jacobson, English Department, University of Pennsylvania
The Mirriam-Webster Pocket Guide to English Usage takes a completely different stance from Strunk & White, understanding the difficulties of making English more gender-inclusive:
They, their, them. English lacks a common-gender third-person singular pronoun that can be used to refer to indefinite pronouns such as everyone, anyone, or someone. Writer and speaker have for centuries supplied this lack by using the plural pronouns <everyone should try it once in their life><anyone who know their grammar knows this>. This use is well established in speech and writing, even in literary and formal contexts. You have the option of using the plural or singular pronouns according to which one you think sounds best in a given context <someone on my left kept bumping me with his or her [their] elbow>.
The Oxford English Dictionary (which is, to be fair, not recently updated – last edition 1993), acknowledges the controversial usage of their in this manner. The OED states:
their 2. In relation to a singular n. or pron. of undetermined gender: his or her (Considered erron. by some.)
Because I tend to turn to Oxford as the final authority (yes, I know my Ivy League roots are showing), and because we’re in the U.S., you should know the 1999 edition of the Oxford American Dictionary provides this definition for their:
their 2. disp. As a third person singular indefinite meaning ‘his or her’ (has anyone lost their purse?)
Finally, while some “grammar purists” take issue with this reworking of “their” as a feminist attack on the English language, this usage is really nothing new. As proof, here are examples from two rather well known authors who appear to have no argument with this construction:
“I shouldn’t like to punish anyone, even if they’d done me wrong”
“It’s enough to drive anyone out of their senses”
–George Bernard Shaw
Originally published in 2000, in a zine that was printed on paper.