Purists who rail about the decline of grammar skills often point to the use of they when people refer to singular pronouns or nouns (anyone, manager, etc.) but a little history might surprise you.
There is a longstanding precedent for using they to refer to singular nouns to avoid the his or her construction. We have been doing it for centuries. My friend Richard Lederer, a language scholar, says Geoffrey Chaucer did it in 1387 in The Canterbury Tales, and the practice continued after that.
In the late 1800s, Lindley Murray, a grammarian and textbook author, decreed arbitrarily that singular pronouns should be followed by his, as in Each manager must submit his plans by Friday, and people began to follow that practice. But many people also continued to use they because it was a tactful and graceful way to avoid using the gender-specific pronouns, as in Each manager must submit his or her plans by Friday. Using they in such instances now has s a longstanding tradition. It’s acceptable to say, If someone wants to take vacation over New Year’s, we can’t stop them, or to say, Every manager must submit their evaluations tomorrow.
You can change the sentence to say, All managers must submit their evaluations tomorrow, or use can use his or her, both of which have been widely used in recent decades, but repeated use of his or her in a paragraph becomes awkward.
So when the grammar cops say you “never, never use they to refer to a singular pronoun, their heart is in right place – they are trying to teach better writing – but they are just parroting what they were taught in school. It has been done for centuries because that is what happens with language. Sometimes we come upon a word or a structure that simply works for us. It serves the purpose, and when enough other people adopt it, it becomes the linguistic norm.