I agree with the post. It's coded derogatory speech while being technically correct. Personally, I would go as far to say it's a dog-whistle and is absolutely a flag, especially if it renders any speech clunky and labored, or side-steps a person's gender transition status.
Also, here's something I've observed that may be relevant.
IMO, most of the time people use gender when telling a story, it's not relevant information in the first place. In light of recent events, public awareness, and politics, non-gendered speech (in English at least) is automatically the most inclusive way to go and it's a good habit to develop. The exceptions here are where it's information that supports the story, disambiguates complicated situations (e.g. talking about a drag persona), or where it's gender affirming in some way (e.g. respecting pronoun preferences).
I see this happen a lot, especially where woman/female is used as extra information when expressing anger, frustration, and disgust. For example, I hear "this woman cut me off in traffic" far more than "this man cut me off in traffic", with "this person" or "a BMW driver" as a maybe-neutral-but-also-likely-male coded qualifier. To me, it suggests a kind of negative bias for gender, which may or may not be unconscious (depends on the person). It may seem like a small thing, but it's freaking everywhere and it's gotta stop.
For the rare occasion where sex or gender supports the story, "my teacher, who is a woman, ..." or "my teacher, (s)he..." does the job. Yeah, it's is a bit tougher on the tongue, but you should only need to say it once for the whole telling.
I agree with most of what you said, but I think using male and female as adjectives is far better than the clunk. Additionally it can help break the whole people thinking of a trans woman as a “male woman” bs. (I have a whole rant about how the “sex and gender are different” thing is often used to ignore the biological realities of the effects of medical transition).
But for the most part it’s smoother to say and can make the fact that you need to mention that you’re speaking about a woman less of a big deal. For example “My cousin, who is a woman, has been having a particularly difficult time finding a girlfriend in her rural town.” Compared to “My employee, a female engineer, is particularly diligent about making sure our products are comfortable for people of a variety of body sizes”
Same goes for race. The number of times a story starts with "this black guy..." and the story has nothing to do with race is way too high. Especially from white people who just say "this guy" if the person was white. It just shows your implicit (or explicit) bias and that you think of someone differently because of the colour of their skin and you're attempting to encode that feeling within your language.
My incel cousin refers to women as "chicks and babes". Then if he sees an unattractive woman, refuses to call them anything.
It's really frustrating dealing with him because he constantly whines about his loneliness and isn't aware how his small mindedness is causing people to bail on him.