Divine right is a concept that came later than the time period BM is based in, and even then secular and ecclesiastical were two very different things. Some random Bishop couldn't just walk into Essex and proclaim that the Earl was no longer Earl, even with a mob. He would have been arrested and executed.
A takeover is a very moot point. Its a King imposing his will on another King. Peasants lawfully raised to constitute an army are totally different than a priest whipping up a mob to oust someone. Its illegal. Hence why you get arrested.
It's not just some random bishop. It's one of the leaders of the faith, who also happens to be a royal of the realm the city used to belong to, not to mention the city's lord and duke himself.
BM priests are not random bishops, especially not elders. They represent the top class of the nobility, like the rest of BM characters.
The comparison to a TO is not moot. In both cases, it's a foreign power using armed commoners to oust the government in place.
I don't really mind the argument that in the chaos of things, the nobles' unit step in to prevent the mob from getting out of control (though I disagree with it anyways), but at the very least, they would never send the person responsible to the dungeons of the government they are trying to utterly destroy.
