I am familiar with 2 clubs in the Jacksonville area.
Both clubs are on city owned property. We cannot stop a non club member from flying at our fields. However AMA membership is required for all members and non members to fly, by both club and city rules.
Both clubs have an area near the freq board for 2.4 users to pin their AMA cards. The reason is simple how do you know if a person is a current member of the AMA if he doesn't post his card.
I remember one year a good friend of mine had his card up in March, but it was for last year, he simply forgot to re-new.