I recently flew as a guest at a field in Florida. As I approached the flightline I was asked very politely if I had both my AMA card which needed to be displayed on my person (they even provided a clip-on clear pocket holder) and whether I had registered with the FAA and to show where that number was on my aircraft. After that I was free to fly following the rest of their typical field safety rules.
One of the clubs I fly with at home required the FAA number be supplied to the club secretary before the gate code would be issued (as well as current club and AMA membership)
Although I have the FAA and AMA numbers displayed on my aircraft, none of the home fields in Maine have asked for the numbers at the flightline.
Jaybird