Everyone seems to know the ideology it's describing when they hear it, and I don't know of another term that does that.
On another tangent: "SJW" was originally coined by social justice warriors as a way to describe themselves. It only became an offensive word once people started lampooning it, but it's still a fair term to use given its history and original intent.
Yes, words only become slurs by being used as slurs, and many words that have become slurs were earlier terms preferred or accepted by the people it is now used as a source against.
Rarely do I see people sincerely espousing what self proclaimed anti-SJWs claim they are. Rarer so do I see it in droves, as a generally promoted claim versus one person or a small group of people.