The other problem with labeling people SJWs - when it comes down to interpreting intent - is that you could label the very people who are calling people SJWs AS SJWs.
Do they repeatedly and vehemently engages in arguments on social justice on the Internet? I've seen some big rants against SJWs that qualifies as "engaging in arguments" about this subject.
"often in a shallow or not well-thought-out way"? Subjective, like you said, but could easily be applied to the anti-SJW poster as well as to the labeled-as-SJW poster.
"for the purpose of raising their own personal reputation"? Again, like you said, subjective and requires guessing as to the individual's motivation but could be applied to anti-SJW posters as well.
And so on. If a definition is so vague that it can be used to define both sides of a debate, then it's useless (at least as far as being used by one side to label the other).