The idea that everyone should be equal in the social sphere

Only eventually. In the meantime, right now, because there are terrible oppressive structures in place, SJ wants explicitly to take power away from some social groups and give it to other social groups. The goal is not NOT equality now, the goal is to create inequality which will compensate for the oppression and, to some extent, balance it.

Look at the lists of demands made by SJ students at colleges (Missouri, Yale, etc.). They don't want to be race-blind, for example. They want to be very very race-conscious to, um, hand-correct for oppression. They want racially segregated housing, FFS.

And, of course, everyone is to be equal except for the enemy which must be cast out and stoned.