I feel like even though there isn't a whole lot I disagree with, there's a fundamental disagreement in framework that's lurking beneath the surface and despite the disagreement in framework, the text is "lucky" enough that the conclusions aren't something that I disagree with. But there's cracks. I'll use this as an example:

In many cases like this, it’s elucidative to make an analogy. For this, let’s talk about bakers. When someone engages with the capitalist system by baking, they tend to form an identity around this baking. That is, having a career in which you bake creates the identity of baker. Similarly, when you engage with reproductive labor in particular ways, you create particular gender identities, both in the ways you conform with the gender that has been given to you and in the ways in which you reject the gender that has be given to you. In both cases, an element of the base is creating within you an identity. Which is to say, your identity stemming from your social position is superstructural.

But this isn't true. In capitalist society, people actually have weak identities related to their occupation. The identity is stronger for labor aristocrats with stable careers, but for your average prole hopping between different gigs on top of various side hustles, how can an job identity possibly form if you have no job stability? And even with labor aristocrats, there's that dreaded phrase "wears many hats," which further erodes identity. In the end, it's because capitalists see workers as any other factory equipment, tools that are interchangeable. They want workers to be blank slate assembly line products that can be minimally modified to perform various tasks. They don't want specialists, but generalists that can molded for various ends like clay.

The real mode of production that cultivated occupation identities was feudalism. If you came from a shoemaking family, your destiny in life was to make shoes for your feudal liege and teach your kids how to make shoes so your kids will continue the cycle making shoes for the feudal liege's kids. A peasant was supposed to know their place as a peasant and raise kids who will also know their place as peasants. Chinese text written during the Spring and Autumn Period went so far as to recommend quarantining people with similar occupations together so if you came from a shoemaking family, you not only were expected to be shoemaker but couldn't even leave the shoemaking part of town so that you'll pick up shoemaking skills faster.

This is a nitpick that has nothing to do with the text, but the entire section no longer makes any sense since the rest of the section builds on the analogy:

So will we force people to stop identifying with being a baker or being a woman?

But most workers don't identify with their occupation in this way, so the question isn't very relevant.

What happens to my identity as a baker once the capitalist system of careers which produced that identity is abolished? This is much more interesting of a question, anyway. Without the enforcement of labor characterized by capitalism, no longer is someone who bakes bread forced into staying within that career.

Except there are plenty of workers who constantly switch jobs and live in precariously (ie the precariat, a term that I'm iffy about) as well as people who have multiple side gigs and hustles.

Over time, the identity of being a baker will likely fade, tho there are many social factors which could allow it to persist, but it would lose its social and political significance. There is no need to enforce the abandonment of the identity of baker to do away with the career system which has produced it.

I mean, it's already fading under capitalism and it has already lost most of its social and political significance. Having a surname Schumaker doesn't mean you make shoes. Starting a shoe-making business with the surname Schumaker doesn't make people go, "wow, this business definitely knows how to make shoes." I would say that capitalism has eroded real identities with deep roots and has replaced it with completely shallow commodifed pastiches of those identities.

It looks like I'm bashing the work, but if you take out everything related to using baker as an analogy in that section, I don't find that section objectionable at all. This is what I mean when I say that their conclusions are reasonable, but the framework to get to those conclusions is not good imho.