I am in need of distraction, so I will spend a little time translating this paragraph to try and make sense of her argument.
The anti-gender ideology movement, a global movement, insists that sex is biological and real, or that sex is divinely ordained, and that gender is a destructive fiction, taking down both “man” and “civilization” and “God”.
She is making a number of claims here, the first being that there is one identifiable, global 'Anti-gender ideology movement'. She immediately contradicts herself by claiming that this movement believes that sex is biological and real or that sex is divinely ordained. These are two separate beliefs, neither of which follows from the other.
She suggests that this one movement believes that 'gender is a destructive fiction' which is 'taking down' (I presume this is 'attacking') 'man' (by which I am guessing she means humanity - not a terrifically feminist styling there, but she is setting up a straw man, so I suppose she is caricaturing her opponents here) 'Civilization' and 'God'.
Butler is very keen to tie anyone questioning gender ideology to religion, which I personally find extremely amusing, as most of the genderist zealots I know personally are members of the progressive parts of the Christian church.
Anti-gender politics have been bolstered by the Vatican and the more conservative evangelical and apostolic churches on several continents,
This claim is fascinating. The influence of the Vatican is pretty much confined to Roman Catholics, and from my admittedly somewhat remote perspective of catholicism these days, there's rather more liberalism that you might expect. Most of the conservative catholics are just cockahoop about the Texan heartbeat bill anyway, so bolstering the campaigns of feminist women seems pretty low priority, really.
Conservative evangelical? Maybe some. But please, look up Kimberley Shappley and Brandon Boulware, two conservative Christians in the US who now have influenced US policy towards gender confused children like their own, who were GNC male children that they both attempted to force into male stereotypes before relenting and accepting that their children were in fact girls after all.
I've no idea what she means by apostolic. I suspect she is referring to pentecostal style churches, which often use 'apostolic' in the individual church name, but apostolic simply means 'a messenger sent', and in fact, is often used of the Catholic church she's already referenced. So she's basically just using a few religious technical terms she doesn't understand to make herself sound like she knows what she's talking about.
but also by neoliberals in France and elsewhere who need the normative family to absorb the decimation of social welfare.
Sharp pivot here from the religious into French and other Europeans worried about sustaining the welfare state and therefore opposing gender ideology because they need a 'normative family' structure. I am guessing her idea here is that a normative family functions as a primary care set up for children and the elderly.
I think that's an interesting shift of focus, because she's clearly setting up straw men opponents here, so the question she should really be answering then is - why is the normative family a problem?
I might even agree that relying on a normative family structure to cover the decimation of social welfare is a bad thing, but from a feminist perspective, the issue is because the bulk of that cover and care of the young and old will fall on WOMEN, the female sex that she is spending all her time and effort trying to pretend don't exist.
None of her pretentious wordplay helps those women. They will still be shouldering the burden of a gendered system, because everyone will still know the group which is expected to do all this, even if we don't call them women any more.
TL;DR Butler thinks that there is one global anti-gender ideology movement that is conservative religious in character and believes sex actually exists, and is ordained by god, and is being pushed so that governments can cut welfare and rely on traditional family set ups instead.
There's so much question begging and strawmanning it's almost impossible to get to the heart of it, but she is basically suggesting we are traditional fascists in the Italian Fascist Party/Nazi party milieu of 'kinder, kuche, kirche', but she's based that on paranoid fantasy rather than actually engaging with any of the feminist critiques.
This is what I meant - her arguments are shite, even when you boil away all the egotistical dross, because she hasn't tested them against the actual opposing view, so all she's doing is shadow-boxing an imaginary fascist.