[Petrosius]

The parent may not have wanted the child’s sex reported, or just stayed away from reporters altogether.

Then the reported should have just said "the child."

The article you referenced shows that the singular "they" was considered incorrect until recently, i.e. until pushed by members of the "gender neutral" LGBT crowd. If they can advocate for its use, those who do not accept their ideology can advocate for its incorrectness.

[Jamestown1630]

No, the article indicates that it was in common use in English until the 1700s, when some began to object to it. The modern use of it to specifically avoid recognizing biological gender is what is very new.

’This use of singular they had emerged by the 14th century, about a century after the plural they. It has been commonly employed in everyday English ever since and has gained currency in official contexts. Singular they has been criticised since the mid-18th century by prescriptive commentators who consider it an error.'