Word for seeing small differences between groups, when you're a member
You could call such a person a splitter:-
a taxonomist who classifies organisms into many groups on the basis of relatively minor characteristics [The Free Dictionary]
in contrast with the person who cannot or does not discern small differences, who would be called a lumper:-
a taxonomist who classifies organisms into large groups on the basis of major characteristics [The Free Dictionary]
I'm not sure this is specific to someone who is a member of such a group, though.