it means that some people who read what you write will judge you negatively if you use prescriptively-frowned-on things like singular they, and---all other things being equal---this could conceivably tip the balance in favor of another candidate for a job or for a place in a selective graduate program, or in favor of a competitor's product.
I don't necessarily buy the whole, "how are you going to get a job speaking like that" argument. Let's face it, grammar proficiency is a requirement for very few jobs. Yes, if you want to get a job in communications, especially as an editor, you'd better not have these kind of things on your resume. But otherwise, the chances a potential employer is going to throw out your resume because of singular they are pretty slim.
I think the reason this argument gets floated is because it comes from people who are in the types of careers where grammar is important.
*I'm not sure what was behind the hubub. I did get a call from young Eric earlier in the week. It was a little hard to understand, what with the Drone Man remix blasting in the background and his slurred speach (you know how