Ironically, the social changes in gender expression you’re referring to are actually premised on the opposite of the assertion you’re making. They posit that gender expression is biologically rooted—because otherwise it would be within the purview of society to regulate it as a matter or culture or individual expression.
My entire point is that’s the morally and legally correct framework, because we shouldn’t be using scientific determinism to make decisions about how individuals with free will and rights can express themselves. The article is correct to have the disclaimer, in this light.
By contrast, what you call the “mainstream liberal interpretation” is actually the radical position. It rejects society’s right and prerogative to impose norms and regulate voluntary self-expression. What generates concerted opposition from conservatives and moderates is the feeling that liberals are using sexual minorities as a vehicle for loosening restrictions on voluntary behavior.
You’re correct the two positions lead to the “same” outcome—but only initially. Eventually, a conflict arises between liberals, who want sanction for a broader range of voluntary self expression, and gay or trans people, who often simply want to fit in as best as they are able. You’re seeing that conflict of interest play out right now. Bostock, which granted equal civil rights to trans people, was immediately accepted by the majority of conservatives. That caused liberals to pivot to causes like drag shows involving voluntary non-conformance, which generated immediate backlash and opposition. For the reasons you explain, liberals can’t tell the difference—to them, it’s self expression, whether it’s voluntary or biologically rooted. But to everyone else that makes a huge difference.
There is a huge wave of anti-trans laws being pushed through by conservative elected officials at the state level right now. They're specifically attacking trans children and school policy, as the soft underbelly that gets conservative parents riled up for a culture war and which is legally more vulnerable.
The culture war came later, when liberals tried to use trans people to promote their own view—which you aptly characterized above—that people should be allowed to express themselves free from traditional social norms and roles. Liberals rushed to promote things like drag shows, which have nothing to do with trans people, and everything to do with voluntary self expression. As RuPaul (a cis man) put it: “Drag says 'I'm a shapeshifter, I do whatever the hell I want at any given time.’” That liberalism is what has “conservative parents riled up for a culture war,” when they mostly didn’t bat an eye at actual advances in trans rights.
I don’t think anyone claims it is completely deterministic.
But it is very significant, to the extent that is may as well as be completely for purposes of discussion or publishing papers.
While there are female lions that act in an atypical manner, the vast majority act similarly enough to say something like “female lions hunt for the pride” without need an asterisk.
The problem is there are a ton of people who try to use that fact to justify forcing everyone to fit the typical trend. "Most people are right hand dominant, so everyone should learn to write right handed or be punished" is the milder historical example. The worst case scenario is "it's legally defensible to murder someone because they don't conform to expected gender roles" https://www.americanbar.org/groups/crsj/publications/member-...
Conservatives trying to use biology to argue that gender and sex are fully equivalent is akin to 19th and 20th century attempts to use evolutionary theory to support racist social policies. It's not only wrong morally, it's bad science.