from the OP > It stands for “emotional quotient” and they ask you a bunch of questions about diversity, feminism... They watch your responses for tone and vocabulary and can veto your hire if they deem you insufficiently enthusiastic.

It sounds very much like your opinions on current political topics.

I don't think the latter* is illegal because it's not discrimination against a member of a protected class. That doesn't make it okay or that it couldn't lead to other trouble.