“Gender-neutral pronouns are no big deal – people have been using the singular they for centuries.”
It’s definitely true that a singular they has been firmly established in English grammar since at least the time of Chaucer. But people who raise this point are misunderstanding the issue. With the exception of a few obnoxious pedants, no one is actually opposed to the use of they and them as singular pronouns in the course of natural, everyday speech. What people are concerned about is the use of these pronouns in a declarative sense – that is, the application of gender neutral terminology as a way of asserting that someone is actually neither male nor female. These two motivations for using they and them are obviously different, and it’s dishonest to pretend objections to one are really objections to the other.
As an analogy, consider the practice of referring to boats as she, which also stretches back for centuries. We all understand that this is simply a linguistic convention; while it may have roots in sailor’s misogynistic attitudes, it was never meant to make any sort of factual claim about a boat being literally female. If someone today did make that bizarre claim (and, as a result, demanded that we refer to his boat with female pronouns), could he defend it by pointing out that sailors in 1800 also called their boats she? Of course not! By the same token, the fact that natural English speech occasionally omits gendered pronouns as a matter of convention has no bearing on whether it’s appropriate for someone to claim they are literally neither male nor female. These are two separate issues, and it’s the latter that concerns so many.