"Joe Sixpack" is a very average fellow; whose commonness is summed up as one who drinks beer as opposed to fine wine. The term can be used in discussions of demographics and marketing: "This advertisement [or political speech] may appeal to doctors, attorneys, and professors, but how will it appear to Joe Sixpack?" Your quote comes from a description of an American-born Muslim cleric. The news story is pointing out that, although a Muslim (which many Americans find unfamiliar and exotic), the cleric engaged in activities normal to Americans (fishing, silly investments) and used American slang (as opposed to reading ancient prayers) in his sermons. In short, he appeared to be part of, and in harmony with, American culture, increasing the contrast to his later activities.

I had to check "Joe Sixpack" also - it's a very American-type phrase. A 'sixpack' is a six-pack of beer It can also mean defined abdominal muscles, ie. looks like a six-pack of beer. Joe is a common name, so "Joe _____" means a generic guy from/about/something to do with _____. Examples: Joe Moneybags (typical rich guy), Joe Hospitalworker (typical guy who works in a hospital), Joe Blow (anyone). Joe Sixpack is a typical beer-guzzling guy. Not very active, not many ambitions and maybe not very smart. A fictional guy to make the average person feel a little superior, maybe. So the speaker talked about Joe Sixpack while he was lecturing - calling the lecture a "sermon" gives the idea that, like in church, you are not allowed to interrupt or question. "Dropped references to ____" means Joe Sixpack was mentioned in passing, not the focus of the talk but included to make it seem significant. As though bulking up the argument with incidental details.