That is an assumption on your part with no evidence to back it up.
While I am not a fan of the AFA I could not find any reference to where the AFA has ever called for canceling, only boycotts. It does this by simply advising its 3.5 million members which movies or corporations do not hold to their values.
As far as not having social power, the AFA owns 200 American Family Radio stations in 33 states, seven affiliate stations in seven states, and one affiliate TV station (KAZQ) in New Mexico.