Everyone should be careful to use a singular pronoun with singular nouns in their writing, William Safire says in his 15th rule for writers.
If he were writing this today, though, his statement might not get any attention. Using third plural pronouns as gender neutral solutions is becoming more and more accepted. A couple of factors come into play. One is discrimination by always using the male pronoun, another is that not everyone is comfortable with their gender.
For a while, there was a movement advocating using new, made-up words, such as ze, ne, ve, and some others. I haven’t heard anyone mention them for at least two years now, though.
Another solution might be to call everyone “it” instead of “he” or “she.” That doesn’t seem right, though, does it?
Whoever invented the English language (all those millions of people over hundreds of years) just plain forgot to put in a neutral third person singular pronoun, and that makes it hard! Okay, that’s inaccurate. English used to have them, but they’ve fallen by the wayside. “Ou” and “a” are mentioned in this article.
So, since we DO have a neutral third person plural pronoun, it’s getting used more and more when we want to leave the pronoun non-gender-specific. I’m a fan of English language evolution so it doesn’t bother me. In fact, I like it!