Look it up. "Impervious to" is an idiom. It means "unable to be affected by".

Example given in my dictionary: "he worked, apparently impervious to the heat"

So when he says the person he is looking for "must . . . be impervious to listening to thousands of B-S stories" he is saying they "must be unable to be affected by listening to thousands of B-S stories". It fits.

It's a joke anyway, but he is saying that someone who can't be unaffected by listening to thousands of B-S stories probably won't like the job.

---- Hugh