Sure, and political/social movements exist which pursue all of these goals. But the underlying moral principle is very much not a matter of ideology or any political "plank", even though 'left-wing'- or 'progressive'- leaning folks are perhaps more likely to care about it in a political sense. Jonathan Haidt is of course very clear on this, and the general idea is older than Haidt's work - check out George Lakoff's Moral Politics or Jane Jacobs's Systems of Survival.

This is probably one reason why the so-called "SJ movement" went so clearly astray in trying to piggyback on any and all of these quite diverse causes, and somehow join them all in some kind of 'big tent' movement. It doesn't work like that - 'big tent' organizations are always a result of coalition-forming within existing civic institutions and processes. Movements need more flexibility, as well as a stronger commitment from their participants.