If your homosexuality, which is biologically rooted, is associated with behavior changes, doesn’t that support the conclusion that gendered behavior is rooted in biology rather than socially constructed?
The question isn't "is gendered behavior rooted in biology?" it's "how much / to what degree?" and the honest answer is, we don't really know with confidence, especially when it comes to humans. The fact that Western culture seems to be currently undergoing a Cambrian explosion when it comes to gender expression contributes to how hard it is to answer this question. Unfortunately that's also why people are anxious and waging culture wars about it.
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 the radical position. It rejects society’s right and prerogative to impose norms and regulate voluntary self-expression. While a minority of conservatives will resist any changes to biblical categories, what generates widespread reaction across multiple groups is the feeling that liberals are using sexual minorities as a vehicle for loosening restrictions on voluntary sexual behavior and gender expression.
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. Liberals can’t tell the difference—to them, it’s self expression, whether it’s voluntary or biologically rooted. But to everyone else, it makes a huge difference whether someone is thumbing their nose at society’s rules, or trying to exist in society the way God made them.
Conservative groups have sued to get religious exemptions to Bostock (https://news.bloomberglaw.com/daily-labor-report/religious-g...) which is particularly pernicious given the number of religious organizations that operate large employers like hospitals.
Just one Tucker Carlson clip (https://www.foxnews.com/video/6324164359112) shows how American conservatives are continually frothing at the mouth about trans rights. There is a related 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.
You can understand the “culture war” by applying your own description of the “liberal interpretation.” As you aptly summarized, liberals don’t care about biological determination because they believe in people being free to express themselves without being limited to traditional norms and categories. It was when liberals started to advance that view—for example by promoting drag shows, which are about cis men dressing up as women as a form of self expression—that they triggered the culture war.