You could argue though that it's only complex because we (collectively) decided to complicate it in order to accommodate the preferences of small subsets of society. In some other country, society might collectively decide not to accommodate said wishes and instead treat sex and gender as immutable and indistinguishable. Such a course would result in a simpler classification system: XX = female, XY = male, anything else = unclassified (genetic defect handled on a case-by-case basis).
There are a a few pretty big upsides I can think of to using a simpler social gender classification system: less social friction/discord/controversy (too much of this and your country falls apart and everyone is worse off), less social confusion/cognitive burden (pronouns, as one example, have basically become a third name that you have to memorize in addition to first and and secondary names whereas they used to just be a derived property that you didn't have to memorize).
This system can break down for some trans people (although I bet most make excessive effort to present as their preferred gender), but it also breaks down for effeminate males and masculine women (and I bet this is the larger category). Despite these difficulties, it's worked for literally all of history until people started pretending they don't know how pronouns work. Test it yourself by taking a look at Lynn's picture and asking which pronouns you'd use.
I'm not sure how invoking genetics simplifies anything. Have you had your sex chromosomes checked? I haven't, and triple-X and KS are often undiagnosed! I'd hate to have to update my drivers license to "unclassified" in my 30s.
I actually don't really care too much which classification system is used (chromosomes vs. observable genitalia at birth vs. something else), I just think the pros of collectively treating certain aspects of identity as immutable such as gender, race, and possibly even name, outweigh the cons of making a tiny fraction of the populace slightly more uncomfortable.
I'll be honest. I'm confused.
But to directly address your point... the main difference here is that "dead names" and "dead pronouns" are considered harmful and/or offensive and are therefore actively hunted and scrubbed from history by activists, unlike maiden names which are considered benign.
Evidence and data seems to support this as we learn and discover more.
And, gender aside, the most important thing to consider is the existence of intersex people, the diaspora of their bodies, and to consider how you think we should talk about them. Sex is, even outside gender, in fact not immutable. It's biology. These people are also historically denigrated.
Please imagine how ~150 years ago we collectively thought (and some people still think) that a person's race determined their intelligence. Historically "fundamental truths" usually end up with people being thought of as subhuman. The "fundamental truth" of sex, as it's presented by those who consider trans folks not people, is the same sort of truth. Biological sex is a spectrum, demonstrably. Gender is also demonstrably a spectrum. I don't care what people believe sex is or isn't. I care that we treat everyone, no matter how "weird" with respect.