No, you don't have to be an AAFP member. AAFP has a lot of CME activities and educational materials, but you can find all of that elsewhere for cheaper. I never renewed my AAFP subscription after residency, and I'm doing just fine. I'm ABFM certified, and that's all you need. ABFM has lots of certification activities that count for your CME. Anything else you do, you just fill out their form and get it recorded.
You are in no way obligated to use or record CME through AAFP. They have nothing to do with your board certification and are a completely separate business entity, and quite an expensive one at that. In my opinion, you are paying mostly to fund their extensive state and national member groups and their CME activities, which is fine, but so far I've found that I can get just as good or better CME elsewhere. I have nothing specifically against them and they do advocacy for family docs, etc...but the price is just too high for me as a young physician with a family to support in a lot of debt. I only have so much CME money to throw around each year, and an AAFP membership would mean giving up other opportunities for local, homegrown CME in my community.