The Griffins have broken the fourth wall on various occasions, and some of their jokes seem to have been written only to amuse the audience, they don’t make any sense within the situational context, what does that suggest? The Griffins are in a reality show shot in studios and outdoors sometimes with hidden cameras and sometimes with actors playing different characters, for example Mayor West may not be the real mayor. Aside from the direct social commentary spoken by the characters, which seems less cringe worthy if you buy the reality show idea, Family Guy comments on audiences that will not be entertained without sex, violence, and madness. Billionaire Sociopath MaCfarlane -in the context of the show- drives the Griffins around creating his show which earns him millions. We know Peter Griffin is a buffoon who cannot hold a steady job and Lois is unemployed in almost all episodes, so the Griffins need the money to maintain their lifestyle. If I may borrow YMS’s explanation of cool cat and his mom, we can assume Brian is some kind of a furry as well.
The jokes that seem out of place and character in Family Guy’s universe are meant solely to entertain you.