From an article in the Washington Post on this, “The Washington Post does not use the honorific for anyone, including those with a doctor of medicine.”
The last sentence for one. “Forget the small thrill of being Dr. Jill, and settle for the larger thrill of living for the next four years in the best public housing in the world as First Lady Jill Biden.” In other words, put aside your professional experience and training. Just be happy to be a housewife for four years.
It’s not specifically “female”, but unless you are using it as a term of endearment for an ex-lover / member of your crew of assassins you recently tried to have killed in a Quinton Tarantino movie, it’s a bit condescending (and in the movie “Kiddo” was the character’s actual last name).
At the very least, it’s kind of a weird way to write. It’s be like titling your editorial “Loose the Dr, brah!”
I would say that “kiddo” can be misogynist for the same reason “boy” can be racist. The latter is considered racist to use for an adult black man, as you would almost certainly never use it for an adult white man. The same is true here: it would be unlikely that someone would refer to a man of Dr. Biden’s age as “kiddo.” It’s a term mostly used for minors or possibly young adults, and even then only ones you know well.
I also don’t see why Dr. and First Lady would need to be exclusive. If her First Lady title is relevant, I don’t see any reason they couldn’t refer to her as “First Lady Dr. Jill Biden” at first, and then Dr. Biden or “the first lady” thereafter, whichever fits better.
The Washington Post’s policy is not to use the Dr. title for anyone. They say they sometimes slip, but generally, Anthony Fauci has been Anthony Fauci, the governments leading infectous disease expert…not Dr. Fauci.
I’m old enough that I remember when this became the standard. Before this a man might be referred to by just his last name without an honorific, but a woman never was. It was odd to my ear to hear/read a woman referred to as just “Doe.” But I got used to it quite quickly. Now, it’s difficult to remember what it was like before.