For example if current grading practices are based on merit, then it is not equitable, as some students will naturally have higher grades than others. The solution, then, is to change the grading system so that good grades may be "redistributed" to lower performers and achieve a more "equal" outcome.
The article is strongly about more performance-oriented, meritocratic grading, not less so.
It considers this to be a problem of equity since current grading practices (in the opinion/experience of the author, at least) disadvantage certain students who perform better than others but have other problems (less access to tutors, less time for homework, less preparation before class etc).
That's interesting, because this idea is so completely counter to what is proposed in the linked article. The article, if anything, is advocating for grades to be more focused on actual learning outcomes (performance) than is the current default. Many of the solutions proposed (such as getting rid of averaging over the entire course) have the goal of making it based more on merit, not less.
I think this gets to the difficulty, in terms of the overall discussion about race, equity, etc. There are some people who really abuse these terms, and others who simply don't know what they mean, or simply have very different ideas of what terms like this mean. (I see this from people with a variety of ideologies and backgrounds.)
My general conception of equity is about adjusting the system in order to remove unfair (and un-necessary) burdens on certain groups of people.
For example, equitable access to real food requires actual groceries available to people. I used to live in Park Slope, Brooklyn. There were literally five high quality grocery stores within a ten minute walk. Contrast that to other parts of the country where there is no easy access (at all) for people to buy fresh produce. That's not equitable.
Similar for grading: If you go into an algebra 101 class, and you do very badly in your first few weeks, simply because you have a lot to learn, you should still be able to get an 'A' in the class if you fully master the material. Otherwise, it's not equitable.
Equity specifically isn't (and shouldn't) refer to equality, IMO. It should be about removing the often arbitrary burdens that disadvantage some people, and the unfair advantages that only serve to put people in an advantaged position (such as providing better grades to people who already know the material in a class, when final learning outcomes are no better.)
So to me it seems we have a definitional issue with the word. Your interpretation of equity makes sense, and is not something I would be opposed to personally. But then there's the other interpretation (redistribution), which is shared by enough people that it's what I think of when I hear the term.
I don't think there's a right or wrong answer to "what equity means", and it's not a very interesting question anyways. What is interesting is how these two very different ideas became conflated, and how to move forward with the good idea and discard the bad idea.
I suspect they've become conflated in some circles because redistribution is seen as a real solution to lack of equity. Notably, this is literally baked into our system in terms of federal income tax, but many people argue that it doesn't go far enough. For example, redistribution of wealth could result in making childcare available to most people, eliminate childhood poverty, etc.
I don't think that in principal that 'redistribution' is controversial. Every contemporary society has some form of redistribution of wealth. However, many people see proposals around it as extreme. Though, whether the proposals are extreme may depend on one's knowledge of the consequences of action (and inaction), among other things.
This gets sticky, because a lot of social activists get hung up on this to the detriment of making real-progress on things that are not controversial when presented in the right way. I see a lot of calls for "ideological purity" and "absolute dedication to the cause". These calls, among activists, often become central to the conversation, as opposed to specific policy proposals that could make a real difference. Personally, I find it rather upsetting to see this happen, as I really do see the problems that are caused by lack of equity, structural racism, etc. But the way the dominant activist groups push for change seems to be too focused on ideology, as opposed to pragramatic solutions. I see the value in anger, which turns into dedication and motivation, I think that it sometimes goes way too far, and then becomes a form of unfortunate self-sabatoge. Anyways, I think I've digressed a bit.
edit: I should add why I tend to be skeptical of them. It's not just about idealogical purity, it's that in order to truly make progress, you have to reduce the total number of problems in the world. It's very easy to spot a problem - anyone can do that. It's less easy, but still fairly easy, to recommend a fix for the problem. But what's very challenging is to find a fix that does not cause more problems than it solves. It's entirely possible to make things worse, and the best way to make sure that doesn't happen is to be dispassionate. But right now the trend is to lean into passion, and specifically, anger. As you said, anger can prompt action. But the problem with anger is that it's a fire that you can't control, especially when you're talking about millions of people.
Critical social justice is a portmanteau term coined by Pluckrose and Lindsay that is being heavily pushed by media sympathetic to their brand of culture war. Neither of them are idiots, but equally I don't find either of them to be highly intellectually honest. I recommend avoiding the term CSJ on HN except where we want to talk about Pluckrose, Lindsay and their entourage, since I think the term tends to undermine curious conversation.
To explain it succinctly, I've become wary of a certain group of people attempting to use subtle language choices to slip in their controversial ideas without being noticed. Equity sounds very much like equality, and therefore people are more likely to sign up for it without understanding the difference. It's a weasel word.