Looks like The High Sparrow has you fooled as well
I think the Faith is definitely fighting for power as much as the next faction, which of course mimics religions holding significant political power in medieval times.
Of coure they are, thats not what I'm saying.
Someone as obviously guilty as Jaime shouldn't be walking around, but the faith threaten him with force instead of imprisonment because of plot convenience I guess.
Not to mention Jaime being imprisoned gives them also political advantage.
And BTW your avatar makes me sad D: