What you characterize as the “more extreme leftist interpretation” is actually the more conservative view. You can get most people on board with exceptions to social norms for biologically-rooted differences. Acceptance of same-sex marriage increased dramatically after the push in the 1990s and 2000s to educate the public that people are “born that way.” “Scientific determinism” is the lynchpin of the broad acceptance of same-sex marriage today.
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.