This is fast overtaking 'multiple attackers' and 'who would win out of ali/lee, gracie/old dude, croc/shark, mongoose/stoat, etc/etc' as worst thread ever. It's only a gi, for feck's sake. And if you do have patches on it, they will no doubt be for your club.
I doubt many instructors would give two poos what you're wearing (especially if it's just for a seminar or a few one-offs), but I'd feel a bit of a tit wearing, say, a gi plastered with Royce Gracie patches if my regular club was Barra or whatever. And yes, it's about loyalty. Which is a pretty big part of any sport.