>>You're missing the point here. The object to "their" isn't for mixed-sex groups, but for the singular:
>>
>>Wrong: The player brings their bat.
>>Right: The player brings his or her bat.
>>Right: The players bring their bats.
>>
>>Tamar
>
>Tamar;
>
>I would suggest you missed the point. What was considered "correct grammar" changes with time. Please note I stated the early 1970’s. What seems correct today many not have been correct in the past.

I think you missed the point. Before the feminist movement (which I agree was catalyst for this becoming an issue), my example would simply have been:

The player brings his bat.

because there would have been no consideration of the point that the player might be female. People starting substituting "their" to avoid specifying sex in the sentence. However, that doesn't make it grammatically correct.

Tamar