The New Atheists: this is just my perspective: Started out with becoming aware that New Atheists should cooperate with other social issues, and should try to appeal to people outside of white, educated, ex-Christians, combined with (correct) realization of problems within community: Elevatorgate, skeptics uninterested in actually useful applications of skepticism to social issues, Dawkin's Islamophobia, etc. Meanwhile, New Atheism ceased to be lonely dissent. Bunch of talk happened, some factions adopted intersectionality and kind of just merged with the rest of modern quasiradical/moderate Social Justice, others went contrarian on other stuff and became (un-thoughtful) reactionaries, etc.

My (somewhat fuzzy) criticism of intersectionality is basically that it discourages keeping ones identity small, specifically on stuff that is usual Social Justice fare, and tends to encourage the congealment of a big body of politics where somebody can always spam 'but that doesn't include _' or 'but that wouldn't work for _' whenever they run into an idea they disagree with.

That said, I do think that the basic concept is important and needs to be understood.