Some quotes from that article. Make your own opinion.
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"(white) cis women’s ability to claim a position of vulnerability in this context is, itself, a reflection of the power that (white) cis women have over trans women (as well as racialised subjects of all genders)"
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"It is disproportionately cis people (both women and men) who are dangerous to, and perpetrators of violence against, trans women, not the other way around"
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"which effectively echo the demands of far-right"
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"particularly Judith Butler’s (1990) interventions that theorised binary notions of sex and gender as culturally constituted"
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"…members of a marginalised group and their allies seek to identify, and express anger or frustration at, a harmful ideology that is promoted primarily by and in the inter-ests of those who are systemically privileged as cis (men as well as women)."
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"This does not, however, mean that ‘TERF’ actually functions as a slur"
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"Gender scholars (e.g. Butler, 1990; Laqueur, 1990; Snorton, 2017; Warren, 2017) have shown how biological conceptualisations of sex are mediated by wider gendered as well as colonial and racialised norms"
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"This means that female and male are, themselves, socially constituted categories, changing over time…"
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"there is no single shared experience of female embodiment or ‘womanhood"
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"By appealing to ‘biology’, authorities lay claim to the ‘neutrality’ and ‘objectivity’ of science – a claim that has public appeal even if it has been contested in social scientific and humanities scholarship for decade"
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"the immutability of sex is itself established discursively, via political means"
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"the world of scientific facts is ‘contextual not only in that it depends on who we are and where and when but also in that it is shaped by where we want our “facts” to take us’"
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That's what they say. Make your own mind.
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A sad thing is that this is the current state of sociology. That article has been published in The Sociological Review—a peer reviewed journal.
No wonder there is a replication crisis in social sciences when they allow articles like that.
Let me discuss the details of your argument, as those details are very important. I will present a perspective of how gender critical trans activism might look like and later compare it with your perspective.
From my perspective a gender critical trans activist must make a clear distinction between sex determination systems, sex, different primary and secondary sexual characteristics and different aspects of gender which I gonna list in the next tweet.
Gender consists of (maybe among other things) the expectations and social pressure related to certain behaviours which form a system. That rigid system is considered oppressive by the gender critical movement, mostly towards women.
What is bad is often not the things themselves but pressure to do them and consequences when one doesn't.
E.g. things like make-up. Without gender expectations it could be an interesting hobby or a funny thing to do from time to time.
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Just like any other hobbys. But it's something totally different when there is pressure in the society for females to apply it (it takes a lot of time which can be spent elsewhere) and there are negative consequences, if they don't.
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Things are often neutral (but some are not e.g. extremely high heels are unhealthy), but it's society values that makes them tools of oppression. Societies can make many neutral things into tools of opression.