And military family cards? ABA cards? How about cards from political parties? The corruption is in how the cops react to such things. (Back in the day, the Hells Angels also issued thankyou cards, although how cops would react is questionable.)
Being stopped by cops is about far more than a traffic violation. Traffic stops are the points at which police most often interact with the public. A cop has to decide how much work to put into a stop, how much non-traffic procedure to follow. Is the person dangerous? Do I need to call for backup before proceeding? Do I check to see if the car is stolen? Do I check for license and insurance? Do I check for warrants? Do I check for out-of-state warrants? Is there an immigration issue? Each extends the stop, which nobody wants. A card that proves a person is employed in certain jobs (military) or is friends with a local officer will cause most cops to save time by not running through all the checks they might otherwise run.
Two people go through border security, one just a random person and the other is carrying a military passport. One will breeze through security and the other might not.
You answered a question I didn't ask, which is "what biases are present in the system that exists today". Whether any of what you describe is either just or justified is still not discussed.
Why *should* a military passport (or my relative is a cop, or my government ID, or my Boy Scout badge, or my jacket patch for that band you love, or my sports jersey, or my bumper sticker) alter how someone evaluates whether I have broken a law or pose a security threat?
I'm not asking why fallible, busy, and sometimes immoral people behave as if it does. I'm asking why it should.
These cards aren’t memorabilia, they’re explicitly made to evade punishment for breaking the law. That’s why they have the name: “professional courtesy”, asking an officer not to enforce the law against someone in their tribe.
I don’t think these are just memorabilia- they have that, too, but these were specifically designed to request officers change their professional behavior, hence the name. If they declined to pull over someone with an FOP sticker that’s also bad but there is a better argument that a membership sticker has meaning other than something you keep in your wallet except when you need special treatment from an officer on duty.
