“Silly me… I thought what group you belonged to was determined by your beliefs and actions. I hadn’t realized that it’s all dependent on your headgear. Please forgive the ignorance.”
no, the headgear is an indication of your beliefs and actions
If you saw a person with a streimel you would say he’s from the chassidic sect (not exactly saying he’s a chassid) a black paper kipah is indicative that you aren’t so observant