Yes, of course you’d need to be specific if it was important. I’d use ‘10 parents’ only if it wasn’t important.
Your example isn’t great though. Even if you assume binary gender for all parents in the group, you couldn’t replace ‘10 parents’ with ‘10 mothers and fathers’ because it’s unclear whether there are 20 people or 10. You’d need to be specific (‘6 mothers and 4 fathers’ or the like).
I don’t think your second paragraph refutes mine at all. I obviously don’t agree that it was ‘sorted out neatly long ago’. You could assume that from the fact that I’ve rethought my own behavior. This world would be a much worse place than it is if people never reconsidered whether the status quo from long ago was optimal.
[Edit: I see now that this comment was not on the same branch as the one where I said I’d rethought my own behavior from a default of e.g. ‘boys and girls’ to ‘children’, so I take back the sentence about you not seeing that. The rest stands though.]