Which it is. That we should have "M", "F", and "it's not that simple" doesn't mean that there's no biological sex; it's clearly defined, very heavily regulated biologically, with multiple mutually-inhibitory feedback loops (which maintain the dichotomy)...and it's biology, so things don't always work in the typical way. I agree that "biological sex" can in some cases be insufficiently precise, but it's definitely real. It's just not binary with zero exceptions, and when you get into exceptions, saying "the biological sex is" isn't always the way you should start a sentence that's going to clarify things.

Note that the authors of Hembree et al.--or whoever actually wrote that table if they included it from somewhere else--have no credibility whatsoever when they call out "biological sex" as imprecise, but happily go on to use "cisgender" (ooh--guess what, it's a spectrum! And you're using a categorical variable label for a continuously varying, albeit strongly peaked, variable!). This is outrageously inconsistent. Heck, there's even a reasonable, principled argument to use to avoid "biological sex", and they used this instead! I happen not to agree with that other argument for various detailed biological reasons, but it at least is worth considering.

The reason why "assigned at birth" is misleading phrasing is because we use "assigned" instead of "observed" or somesuch when there's sizable ambiguity resolved by people in authority. We don't say days are "assigned as rainy", even if there are, say, one in five thousand cases where you can't tell whether it was rain or not (and are trying to come up with better ways to disambiguate). In those cases where sex-associated morphology is legitimately ambiguous, then yes, use AFAB/AMAB if that's how it turned out! If there is no X option, M or F is indeed assigned (and sometimes reassigned and rereassigned). I entirely support "sex assigned at birth" and AFAB/AMAB in those cases because it compactly describes the situation.

In almost all other intersex cases (e.g. not Caster Semenya who is XY but 5αR2D(df)), the relevant information isn't AFAB/AMAB. If you are an XXY morphological male, saying that people probably assumed you were an XY male when you were born is, if anything, compounding the error. People said you were male, you look male, so we know what we need to know, right? Nope! Not if it's a medical form.

In the case of trans people, gender expression doesn't match sex (and some sexually dimorphic characteristics may have been changed through hormonal or surgical intervention--yes, this is a sex thing not a gender thing at its core). In this case, the "assigned" is also actively misleading because there wasn't anything arbitrary about the determination (usually)--the physical sex, whether you determine it by karyotype or genital morphology or whatever, was unambiguous. Simply dropping the "assigned" would be fine: "Female at birth", "male at birth".

And in the case of everyone else, "sex assigned at birth" is, again, actively misleading because not only was it observed, not assigned. Appearances were not deceiving.

The canonical advice in UX design is now to use "sex assigned at birth" as the field that asks about biological aspects of sex. This means that it isn't some obscure thing that people hardly ever see. And given that the advice is to have at least three options, one of them being intersex (a subset of which is the only population where "assigned" matters, and which, by virtue of the questions asked, can't be answered on that form!), the "assigned" bit is uniformly unhelpful.

The only thing it's good for is implying that sex--not gender--is a fluid and arbitrary thing, which is starkly in contrast to reality. That, and placating a community that has been badly treated and wants this.

Now, I'm not a huge fan of that opinion piece. For something that is claiming to be concerned with accuracy, it does a woefully inadequate job of talking about all the various things one might want language to describe (e.g. your point 1). And I agree that it was likely intentional (your point 2) given that they had one goal, supposedly, and basically flunked it.

However, trying to attack the article for accepting that biological sex is real is exactly the kind of nonsense that gets some people worked up about this in the first place. A great way to generate extra opposition where there wasn't any before is to indicate that something that is plainly real isn't.