Fourth-wave feminism actually does broaden itself to other culture theory participants, like LGBT+. With its
cyberfeminism sub-category even desiring the introduction or creation of dozens of new (non-binary) genders. But 4th-wave movements are merely one facet of a very complicated feminist landscape.
For instance, a problem that the "gender critical" (GC) branch of radical feminism has with trans-women is that they regard the latter as perpetuating patriarchal gender norms that were used to subjugate women in the past. That includes their feeling or belief that they were biologically predetermined to be female rather than male (have female brains in the wrong body, or whatever). For GC radical feminists, gender is a learned social construct and has no grounding in being fixed by nature.
In terms of GC's historical roots dating back to the '60s and '70s, gender identity is thus an oppressive form of caste or class system that must be eliminated rather than encouraged (or at least be de-fanged to the point of no longer being an obstacle to radical equality).
Shulamith Firestone: "
The end goal of feminist revolution must be, unlike that of the first feminist movement, not just the elimination of male privilege but of the sex distinction itself: genital differences between human beings would no longer matter culturally."
Gender dysphoria is thus tenable and acceptable in GC radical feminism due to gender dysphoria's allowance that this distress can contingently result from social factors rather than innate origins.
Rowling, however, is an eclectic feminist rather than a radical one -- that is, she pragmatically picks and chooses from the whole gamut of feminist philosophy. Ergo, appealing to advocates of gender dysphoria when convenient:
JK Rowling: "
Lisa Littman had dared challenge one of the central tenets of trans activism, which is that a person’s gender identity is innate, like sexual orientation. Nobody, the activists insisted, could ever be persuaded into being trans."
But she's correct (for the most part) when asserting that the gender critical club should (in the context of its ideology) be no more hostile to trans-women than it is to born women who perpetuate classic gender stereotypes that they regard as belonging to oppressive patriarchal tradition.
JK Rowling: "
None of the gender critical women I’ve talked to hates trans people; on the contrary. Many of them became interested in this issue in the first place out of concern for trans youth, and they’re hugely sympathetic towards trans adults who simply want to live their lives, but who’re facing a backlash for a brand of activism they don’t endorse. The supreme irony is that the attempt to silence women with the word ‘TERF’ may have pushed more young women towards radical feminism than the movement’s seen in decades."
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