John Doe “has added new links and updated their profile”
John Doe is an individual. “Their” is plural. I understand they’re trying to avoid “his or her”, but I’d prefer it.
Another example… when someone requests an endorsement, the message comes across as “Can you endorse me?”.
The word “can” implies ability to do something, not willingness. I’d much prefer to see “Would you endorse me”.
There. It’s off my chest now.
"Recognized writers have used they, them, themselves, and their to refer to singular nouns such as one, a person, an individual, and each since the 1300s."
From the same source you reference:
"Most of the Usage Panel rejects the use of they with singular antecedents as ungrammatical, even in informal speech. Eighty-two percent find the sentence 'The typical student in the program takes about six years to complete their course work' unacceptable."
So why not: "John Doe provided new links and an updated profile". Avoids the issue altogether.