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.
I don't know whether anyone noticed my list is basically libertarian. It's a very challenging agenda, but it just covers allowing freedom and protection from violence. It doesn't cover ongoing help for people who can't fully take care of themselves.
A long blog post explains why the author, a feminist, is not comfortable with the rationalist community despite thinking it is "super cool and interesting". It's directed specifically at Yvain, but it's probably general enough to be of some interest here.
http://apophemi.wordpress.com/2014/01/04/why-im-not-on-the-rationalist-masterlist/
I'm not sure if I can summarize this fairly but the main thrust seems to be that we are overly willing to entertain offensive/taboo/hurtful ideas and this drives off many types of people. Here's a quote:
The author perceives a link between LW type open discourse and danger to minority groups. I'm not sure whether that's true or not. Take race. Many LWers are willing to entertain ideas about the existence and possible importance of average group differences in psychological traits. So, maybe LWers are racists. But they're racists who continually obsess over optimizing their philanthropic contributions to African charities. So, maybe not racists in a dangerous way?
An overly rosy view, perhaps, and I don't want to deny the reality of the blogger's experience. Clearly, the person is intelligent and attracted to some aspects of LW discourse while turned off by other aspects.