I work in the nonprofit world, so bear with me for a bit...
The AMA is a 501(c)(4) nonprofit. As such, they can only engage in very specific political activities or statements. (And BTW membership fees and donations to any c4 are not tax deductible.)
Because of this limitation, they doubtless established a "sister" PAC (Politicial Action Committee) organization, which is not limited as to what types of politically-oriented issue ads/statements they can run, and the PAC can directly endorse and support specific candidates.
It is standard operating procedure for 501(c)(4) organizations to share member/donor information with their PAC affiliates. It is also SOP for them to not share that information with other organizations.
I would bet that if asked the AMA folks to remove you from their PAC-sharing mailings/emails they'd be happy to do so.
In any case, you don't have to worry that they're sharing your info with the world at large. AMA has been around long enough to realize that shopping their members to every Tom, Dick and Harry would most likely alienate the members, which they certainly do not want to do.