If you are concerned with the use of non-sexist language, this is one way of looking at it:

Some careful writers use they when the antecedent is an indefinite pronoun (such as anyone) to avoid making a sexist assumption; however, many other people think this disagreement in number is an error. Rewrite to avoid it whenever possible.

Sexist:        If anyone was on top of things, he would know that.
Disagreement:  If anyone was on top of things, they would know that.
Rewritten: Anyone who was on top of things would know that.

[source]

Resty O. of ExpectoRANTS asked this question: Is the pronoun-antecedent agreement rule still valid?

I am asking the question because famous writers and literati I admire and respect are suddenly using sentence constructions that blatantly violate the rule.

An antecedent is, of course, the word that a pronoun refers to in a given sentence.

In the ff. sentence, “Everybody” is the antecedent being referred to by the pronoun “their.”

Everybody is having their own version of fun.

I’ve always thought this construction to be wrong, but, for some reason, it is becoming accepted because respected writers are writing this way.