As per tradition, I'll make it clear that the question in the title is not rhetorical and I genuinely want an answer.
But I think we might, in fact, need a new term to describe the insane wing of the social justice movement. Allow me to exemplify a sort of comment that I keep hearing lately (with only one example because I'm too lazy to look for more). From
Pharyngula:
In my email and on twitter, I get called an SJW all the time, and all I can say in reply is “YES, and proud of it. What’s wrong with you?"
It's not this quote that bothers me per se, it's the fact that I've seen many, many more of its kind. That kind being people who I'm sure are mostly sane declaring themselves to be social justice warriors and finding it ridiculous that anyone would think they take it as an insult.
There's many things one could say about PZ Myers, not all of them flattering. I could understand accusing him of being too aggressive, of being too quick to declare someone an enemy of all that is good and righteous, of not giving a balanced account of things*. But he's not insane. He doesn't declare arbitrary new pronouns that apply only to one person, he doesn't think all penetrative sex is rape, he doesn't declare speaking another language to be cultural appropriation. And presumably he doesn't think he's associating with those ideas when he declares himself a social justice warrior.
Because on some corners on the internet, including FQA, SJW pretty much means the sort of people we quote on
Worst of Social Justice**. But on others, it just means someone who cares about social justice.
And social justice is a good thing! I'm pretty sure everyone or nearly everyone here would agree that racism and sexism and LGBT discrimination and all such things are bullshit of the worst sort. With some disagreements as to the specific degree to which something counts as sexist/racist/etc., but we're all mostly on the same side. And we want people who are on our side and not, as previously discussed, insane, to work with us rather than against us. To not get sidetracked over pointless bickering over whether the fact that you called someone an SJW means you are a racist homophobic MRA who possibly kicks puppies for fun (try telling me it doesn't happen. I fucking dare you). In essence, we want not to get in fights people who are basically our allies but just happen to use a slightly different dictionary.
And someone will say that there is already a perfectly suitable distinction between sane SJAs and insane SJWs. As it turns out, though, having two very similar terms to specify a subjective difference in two superficially similar subgroups is not the path to clarity***. Inevitably, you're going to have things that people will disagree over whether they are sane or insane. And then you're going to have people who didn't receive your copy of the Internet Dictionary wander in on a conversation, see you call something they find sane to be SJW, and deduce that it's just a word that MRAs use to describe feminists or something.
Which of course is the other part of the problem. Some people think
all social justice is insane, and as it turns out they are also out there on the internet using words. We're not gonna get them to work with us here.
TL;DR: The SJW vs. SJA distinction is not universally understood or recognised. The term "SJW" starts pointless fights with reasonable people who would naturally be our allies if not for the fact that they think SJW is a term bigots use to insult non-bigots. For pragmatic reasons of communication and movement cohesion, I think a better alternative is needed. I would suggest one but my brain is empty right now.
EDIT:
Magus suggested "radflake". I like it. Consider it my official new term for them.
*I'm not saying I necessarily think that, I personally like his blog. But I could understand someone thinking so.
**While I'm asterisking my disclaimers, should mention that, no, I don't think everything in that thread is insane or wrong, and I have said so many times. I still agree with the spirit of it.
***I have no idea why there are so many words that start with 's' in that sentence.
I expect someone, somewhere is going to complain that my use of "insane" in this post is ableist. To which my only reply is, give me a better word and I will stop using it.