MtheGM, I agree that satirists can be blamed if a typical audience is likely to misunderstand them, and all the more so if they are actually under suspicion to promote those prejudices secretly. I cannot judge whether this holds in your case, I am just positive that careful and experienced readers will discover the satire alright.

The examples John Cleese was referring to - mainly "Fawlty Towers" - were also often criticized for the opposite reason: being too obvious and simplistically pedagogic. He was definitely not secretly endorsing those prejudices. Hard to please everyone. (That series featured a retired soldier who perfectly represented the "innocence" mentioned above, meant to be self-revealing - sadly going totally amiss with many watchers, even those who understood the idea behind the "Fawlty" character played by John Cleese. Watch it on YouTube.)