The characterization on that page is not good: virtually no one disagrees with "the ability to learn grammar is hard-wired into the brain". The substantive disagreement is whether grammatical categories and relations (or other knowledge that helps the child induce such) is hard-wired, or whether more general-purpose learning mechanisms are sufficient to abstract this structure from the environment.
>virtually no one disagrees with "the ability to learn grammar is hard-wired into the brain".
No, this is exactly where the field is split. Chomsky says that if a child socializes with people speaking a language with each other, the child will learn that language without teaching, punishment or reward. I.e. the human mind is not a blank slate buy has innate capabilities. Ideologically, this is an individualist take on linguistics.
The other side says that children have to be taught to speak a language properly and that language is difficult. Ideologically, this is the collectivist take on linguistics - children are blank slates to be filled in by society.
The people that have a problem with Chomsky's ideas are authoritarian collectivists. It's not about science.
You're making a straw man caricature out of the nativism detractors. Current researchers do not claim that first language is taught, that's why the field is called language acquisition regardless of whether one subscribes to nativism. The more nuanced non-nativist theories argue that grammar learning employs domain-general cognitive mechanisms, rather than language-specific innate grammar knowledge or principles. It's quite a stretch to connect any of this with political ideologies.
