Gu Hang had never underestimated the state religion; even though they lacked nominal military force, their greatest weapon was influence. And that in itself was terrifying.
If the Pontiff of the State Religion, or a particularly influential Cardinal Archbishop, truly got tough and declared someone or someplace heretical, or made a proclamation about a region occupied by aliens, the Chaos Cult, the onset of a crusade was very likely.
The bishops might not have regular armed forces other than the Sisterhood, but they could invoke the name of a 'crusade' to rally all the governors and imperial military forces across several star sectors.
And when they wanted to do so, they often succeeded. There were many such instances in the history of the empire.
This was not a matter of authority, commands, or coercion, but rather the persuasive power brought about by influence.
