I am not familiar with what the term Critical Grammar actually means, and I'm sure it can mean different things, but as far as I can see, something it claims (or Rather Rutger University claims on its behalf) is to be not about lowering standards in order to increase diversity and inclusion, but merely about
understanding the ways in which language (specifically grammar I suppose) has political and social implications, including in relation to things like power, hegemony, inclusion and diversity, in order to then make
informed, critical choices about grammar.
This seems to be borne out in the (previously quoted here) part of the Rutgers email under the sub-heading
"Incorporating 'critical grammar' into our pedagogy", when it says:
This approach challenges the familiar dogma that writing instruction should limit emphasis on grammar/sentence-level issues so as to not put students from multilingual, non-standard "academic" English backgrounds at a disadvantage. Instead, it encourages students to develop a critical awareness of the variety of choices available to them w/ regard to micro-level issues in order to empower them and equip them to push against biases based on "written" accents."
In which the second, green part contrasts with the first, red part, in such a way as to suggest that lowering standards (specifically the lowering of standards which is apparently already 'familiar dogma') is pretty much the opposite of what is intended.
Ok, so far so good. Standards are not under threat, in fact the University, using a Critical Grammar approach, is going in the opposite direction.
But after googling, specifically with the intention of finding a concrete example of Critical Grammar that might clarify, I found this article, which as far as I can tell, promotes a Critical Grammar pedagogy:
The Writer and The Sentence: A Critical Grammar Pedagogy Valuing the Micro
https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1350&context=open_access_dissertations
Here is an excerpt:
""Ivanič reveals this in her case study of John, who is described as “highly involved with Aids campaigning”. John’s example, really a small detail in Ivanič’s larger study regarding relationships between discourse and identity construction, involves a decision-making process in a medical ethics paper, a process that only becomes conscious thanks to Ivanič’s awareness. She asks John about his choice to use the word “Aids” in this paper, asking him about his decision to represent Aids as a word rather than an acronym. She explains that she knew there was a difference between how writers use this word, did he? He says that he was not aware of a political difference between the choices. Ivanič shares that she knows that the word Aids is one way to represent the social context of the disease, and not its biological impact/AIDS. After learning about the difference, packaged in the word/acronym Aids/AIDS, he tells Ivanič he will “continue to do so,” which I take to mean, he will continue to write the word Aids. While John’s choice does not change, his understanding of what this choice means in its given context does change, and in this way, John’s choice of Aids is a critical choice."
Which, unless I'm misunderstanding it, is permitting John to make a 'critical, informed choice' to continue using the incorrect term (Aids rather than AIDS)? If so, this sort of Critical Grammar (which seems to be the same sort as in the OP article, in that it's about critical awareness) is not doing what it says on the Rutgers tin.
Unless of course I am wrong, and there is such a thing as 'Aids (capitalised) campaigning' in the medical ethics sphere regarding AIDS, to represent the social context of the disease rather than the biological. If so, that would be news to me, if not to Ivanič. Although she is the professor of Linguistics and acclaimed as a prominent expert on literacy, not me.