The main point of the show was to insult AA and the attitude that alcoholism is a disease that needs a cure from God instead of, as Stan said, "Just quit drinking." Before AA, Stan's dad drank, but wasn't an alcoholic, just stupid enough to drink and drive once. AA really messed him up by telling him he had a problem that he didn't have, which actually turned him into an alcoholic since he now has a disease, so he can drink all the time and blame it on the disease. Then they told him it could only be cured their way, religiously. This mirrors the Scientology episode, which was mentioned ("I know about cults. I used to lead one.").
A sub point was to make fun of all of those people who flock to be cured by bleeding statues and faces on toast.
An even lower point was how church decisions on what is and isn't a miracle can be strangely arbitrary.