I don't know a single generative linguist who is committed to the claim that grammaticality is binary. And there is lots of published work in generative linguistics that explicitly does not assume this. Where are you getting this idea from, exactly?

>language is essentially algebraic,

Not sure what this means. If it just means that sentences have structure, then yes, generative linguistics is committed to this obviously true claim.

>He repeatedly dismisses whole subdisciplines as "uninteresting," but in context those complaints don't mean "uninteresting to me," they mean "worthless."

He's entitled to his opinion, no? It's not as if no-one ever criticizes his work.