English is my first language, and I think it sounds fine:
> A CEO ... . Like it or not, their job is to protect the company, not the users.
It wouldn't sound as correct if the subject was a specific person. In that case the gender-specific pronoun would be better.
> Marissa Mayer, as CEO ... . Like it or not, her job is to protect the company, not the users.
Even so, use of 'their' in the latter example would still be acceptable, if a little odd, because it's referring more to the role than the person (I think).
[edit] for what it's worth, I think you're overwhelming underestimating the percentage of people who think more gender-inclusive language is a useful thing.
That said, I didn't suggest the option because I was trying to make that point, I suggested it because the parent was dealing with a situation (unsure of gender of the CEO) where use of the singular they is really effective.
> A CEO ... . Like it or not, their job is to protect the company, not the users.
It wouldn't sound as correct if the subject was a specific person. In that case the gender-specific pronoun would be better.
> Marissa Mayer, as CEO ... . Like it or not, her job is to protect the company, not the users.
Even so, use of 'their' in the latter example would still be acceptable, if a little odd, because it's referring more to the role than the person (I think).
[edit] for what it's worth, I think you're overwhelming underestimating the percentage of people who think more gender-inclusive language is a useful thing.
That said, I didn't suggest the option because I was trying to make that point, I suggested it because the parent was dealing with a situation (unsure of gender of the CEO) where use of the singular they is really effective.