"Singular they/their" has been part of English since the 13th century or earlier. Used with the highest frequency by a great many major English prose authors, and even by Shakespeare on a couple of occasions:
God send every one their heart's desire!
[Much Ado About Nothing, Act III Scene 4]
There's not a man I meet but doth salute me,
As if I were their well-acquainted friend.
[Comedy of Errors, Act IV Scene 3]
And of course the illustrious stylist Oscar Wilde:
Experience is the name everyone gives to their mistakes.
http://www.crossmyt.com/hc/linghebr/austheir.html