MattG
Getting familiar with the group...
I don't know of many car dealer service and/or parts departments that don't take AMX (never saw one that didn't and I owned Toyota's for the last 17 years and Honda before that). I know at one time AMX was not accepted everywhere, but it is increasingly unusual to find a retailer that doesn't take it (unless they are very small).
I would bet a lot of money that percentage of Hyundai owners who have an AMX card is lower than Toyota or Honda owners on average. Obviously that would not be true of Genesis owners, but Hyundai still sells a lot more of the other cars.
Way to casually insult a whole lot of people!
Amex processing fees tend to be a little higher, so this is going to primarily be about volume. Bigger dealerships will get better rates, and so it will make more sense to accept more cards. Smaller dealerships, or ones that are not part of larger dealer networks, will often limit their card choices because of those fees.
If you want to offer a complaint that a dealer does not accept a particular brand of plastic, that's fine, since it is a convenience thing. Jumping to conclusions about a whole group of people based on a single external identifier, though. . . what up with that?