This article insightfully analyzes how oppressive regimes seek to marginalize people using language tests. I would definitely like to read the book you cited.
Yes, grammar has been used to oppress people. Linguists have demonstrated that all ideas of correctness in language are arbitrary. The one dominant form of a language deemed “standard” is the one spoken by people with the most power. Others are marginalized because they speak or write a different language variety.
Grammar tests to determine voter eligibility are fascist.
Although the notion of a standard form of a language is based on arbitrary criteria, I don’t believe that the use or teaching of that standard is oppressive; it’s the individuals promoting that standard in an oppressive way that are the the problem. We shouldn’t jump to destroy the concept of standard English, for example, as an example of “colonialism,” as some people are calling for. I think we just need to appreciate the infinite creativity of language.
Oh, and we also have to stop oppressing each other for any reason, including language.