My noble friend highlights the tension between etymological orthodoxy on the one hand and political correctness on the other. I was brought up to believe that “they” was a nominative plural pronoun and “he” or “she” was the singular. But that was a long time ago; popular usage has moved on, and so have the grammar guides. Indeed, the singular “they” is now used in legislation. It was used in the Terrorism Act. But, to go as far as my noble friend has suggested and use “they” in all circumstances would, I think, be a step too far. In many cases, the use of “a person” would do just as well.