West Wing reasoning behind mocking people who say "there but for the grace of God go I?"

Josh is referring to himself when he says "there but for the grace of God go I". He is joking that he might have been the sort of person to end up on a Citizen's Stamp Advisory Committee if his life had taken a different path.

By extension he is also mocking the people on the committee, because he clearly prefers the life he actually has. He sees their work as trivial compared to his own, and implies that being on the committee would be (or should be) embarrassing.

Donna is making the same kind of joke.

Essentially they're both saying "haha, glad I didn't end up like those people", while layering a small amount of self-mockery on top, because of their suggestion that they could easily have ended up that way - but for the grace of God.

Neither Josh not Donna are presented as overtly religious characters on the West Wing, so it is also likely that they're using this phrase because it is a common saying in English, rather than attributing their current positions to the literal grace of God.

When people use this phrase they aren't always joking or making fun of people - often they are simply expressing a sense of gratitude that they have avoided a bad situation. But in the specific quotes you included, Josh and Donna (and the writers of The West Wing) were going for laughs.

"There But For the Grace of God Go I" is a sentiment often expressed by those who choose to help the unfortunate - in other words, people who claim to recognize that only good fortune has caused their lives to work out differently to the lives of those in need.

Given the mocking tone that Josh is using, he is probably referring to members of minor social relief committees in government, who are preoccupied with the idea that they are doing good for the unfortunate, and perhaps burnishing their own self-images at the same time. The biblical reference adds an element of pseudo-piety to the mix.

"There but for the grace of God, go I" is a phrase that points at someone less fortunate behind their back, calls attention to their misfortune, feigns pity, and then expresses gratitude to God for sparing the speaker from something He didn't spare the subject from. It is loaded with sanctimony and condescension. The fact that it loosely reverberates with a specific line of scripture that it's meaning in no way reflects just amplifies it's problems.

It is a bit wierd that they made the same obscure and specific joke out of the phrase twice. It's also wierd for me to be posting on a 5 year old thread about a 15 year old TV show but who's counting.