This organization does have connections to Islam. Just the same way that American Family Insurance has connections to WASPS, and Jews, and whoever you interact with. It's not meant to be a negative experience, because the meaning of the word "business" is "busy". You don't have a busy business if you don't interact with people from other ethnicities and cultures.
No, the American Family Association is not connected to Islam, because they have vastly different ways to go about the things they want to happen. Both the AFA and Islam have higher standards for morality and personal conduct than the general American society has, but that is where they part ways. The AFA and Islam disagree on most other major issues.
I do not know of any kind of connection between the American Family Association and Islam. I would say they are like oil and water. One is a far-right Christian-based organization and the other is merely a different religion, so I would be hard-pressed to see what link exists between the two. If anything, there have been blog posts on the AFA website critical of Islam.
Tell them that they are though, I'm sure it would infuriate them. The American Family Association is a bunch of backwards bigots living in the past, I'm sure they'd lead the charge to drive Islam out of the country before they were in any way affiliated with it. The short answer here is no.
The American Family Association connected to Islam. At least anything is possible but I do not think that they are. The American Family Association is a United States non-profit organization that promotes fundamentalist Christian values. It opposes same-sex marriage, pornography, and abortion. Basically, it is a hate group for anything they do not believe in and they are hated for it. I do not like them at all.