Comment with small things:

This new system has a few characteristics which define it. Not all of them developed at once, but they’ve been imposed upon the whole world. They are as follows:

[...]

3. Marriage is an economic contract between a man and a woman. Men and women are supposed to sign an agreement to be faithful and to stay together and violation of that is seen as a breach of contract and therefore bad.

4. Marriage is a personal choice done for love rather than a social choice done for necessity. Gone are marriages for alliances or arranged marriages, for the most part. Marriage is only a choice for the two who are getting married.

Obviously there is some conflict between the ideas of economic marriage and love marriage. The system is in motion; the superstructure shifts focus from 3 to 4 as women become proletarianized. I would have liked to see some exploration.

Since this third class is defined by its difference from those of the first two classes, it is named queer. Queer people are all those who relate differently to the division of reproductive labor assigned to them by patriarchy. Because of the different relations, queer people are inherently subversive to the class system as a whole and constitute the revolutionary class under patriarchy.

if women are the oppressed class, doing reproductive labor without any control over it, why wouldn't women be the revolutionary class? this is like axiomatically saying that lumpens, not proles, will be the revolutionary class that brings about the abolition of the proletariat. some people think so but without an argument I'm not convinced

People whose gender doesn’t match with the gendering of their biological features aren’t exactly new. Many previous systems had explicit classes for people like this, such as the Bugi gender system. These are multigendered systems and they have a space for those who aren’t willing to accept the gender assigned to their biology.

Nitpick: we opened the piece by saying that gender is a superstructure and reproductive labor divisions are the base, and by explicitly repudiating people who think that sex is the material base of gender. So gender isn't "assigned to biology" in these multigendered systems, it's assigned to labor roles.

Gender isn’t inherent, but it spreads by assigning us to a class and forcing us to say yes to that class. “Yes, I am a man. It is who I am and who I always have been. I cannot escape it or deny it. I am a man.” This is nothing but a lie we are forced to repeat. But by repeating it enough, we come to believe it. Gender becomes natural, inescapable, eternal. It ceases to be an imposed identity and becomes an eternal part of who we are.

I don't think this is consistent with the idea of labor role as base and gender as superstructure. Gender can't spread via people internalizing the superstructure and identifying as a man or woman. In this framework gender must spread (or rather maintain itself) by people carrying out the role of gender. I think this section is inconsistent with the one on baking, which is better. People identify as "bakers" not because they think of themselves as a baker and then seek out jobs at a bakery, but because they are economically coerced into wage labor and they end up at a bakery. As the authors write, the superstructural identity of "baker" will wither away once baking is not a job. People really do think of themselves as having a gender. But some Brits think of themselves as "upper crust" and some Indians think of themselves as "Brahmins", and the way to class abolition is not people deciding not to identify as working-class anymore. It's a basal change caused by oppressed people engaging in class struggle and winning. The authors say things like "If everyone says “no” to gender, everyone ceases to accept it, then gender is lost. We find similar strategies among resistance to other class systems." We must be clear that saying "no" to gender has to mean more than just refusing to perform cisgender identity, it has to mean tearing down gendered division of reproductive labor. And if the authors agree, I wish they'd have written more about the specifics of what reproductive labor actually is and how the masses can fight male control of it.