Wrong Gender or Wrong Number?
There are still some grammarians who insist it's wrong to use they, them, and their as singular pronouns when the gender of the person is unknown, as in "Anyone can express their opinion by writing a letter to the editor."
Yet they, them, and their have a long history of acceptable use as singular pronouns, including by esteemed authors Geoffrey Chaucer, William Shakespeare, Jane Austen, Charles Dickens, George Orwell, and many others. According to Rosalie Maggio, in The Bias-Free Word Finder, it was in the mid 1700's that "He was declared generic and legally inclusive of she by an Act of the English Parliament," and grammarians decided it was "preferable to make an error of gender" rather than an "error of number."
Nowadays, I hope there's no one who would argue that it remains acceptable to use he, him, and his when referring to a person who may be female. Yet what are the acceptable alternatives? Constructions such as the horrible "s/he"? Using "his or hers," with the occasional "hers or his" thrown in?
One alternative is to re-write sentences to avoid the need for specifying gender. For example, replace "He who laughs last, laughs best" with "The one who laughs last, laughs best."
Maggio offers a number of other ways to make your language inclusive as well as grammatically correct. I certainly agree with her that one way is to reclaim they, them, and their as acceptable singular pronouns. Given the history of the English language, if anyone objects, well, all I can say is this: "They should reconsider their opinion."