See https://stroppyeditor.wordpress.com/2015/04/21/everything-yo... for more than everything that you might want to know about the use of they as a singular pronoun. Even those who think that they object to it, frequently use it without noticing.

The upshot is that whining from self-important grammarians notwithstanding, English has always had a third person singular pronoun in common use. It has been used in every century by established writers. Indeed frequently by the same people who were saying that nobody should use it. That pronoun is "they".