I'm looking for the term that applies when someone disqualifies another party from social groups membership.
ex: "You're not a real fan if..."
A term that comes to mind is petty or - taken in another direction - discriminatory, but perhaps you are looking for the "No True Scotsman" or "Appeal to Purity" fallacy
No true Scotsman, or appeal to purity, is an informal fallacy in which one attempts to protect a universal generalization from counterexamples by changing the definition in an ad hoc fashion to exclude the counterexample
Person A: "No Scotsman puts sugar on his porridge."
Person B: "But my uncle Angus is a Scotsman and he puts sugar on his porridge."
Person A: "But no true Scotsman puts sugar on his porridge."