The 'new order' needed the support of the Theology Council to validate the formation of Privy Council, they needed the Theology Council to validate the decision to disband the Council of Apostles and raise the Emperor to the station as the only spiritual leader of the Empire.
The 'new order' needed the Theology Council to validate the Moral Reforms.
Something more recent that can be read as Theology Council not wanting anything threatening their place as the sole institution that can interpret the Scriptures and validate religious dogma.
The Tetrimon brought back the unaltered Scriptures to the Empire and the Theology Council did not let anyone else have access to them as they were 'verified', suddenly after the process was finished there was evidence found that the Tetrimon was committing treason against the Empire and decimated completely.
The 'new order' owes their place in the Amarrian society to the Theology Council, of course they would benefit from the fact that the Theology Council would be weaker, but it would mean that the Empire would turn more secular, which is something that the ruling elite does not want.
Without divine mandate to rule, there is no nobility, there is no Heirs.
There is no Emperor.
That mandate comes from a specific way of interpreting the Scriptures.
To keep the status quo the access to the Scriptures has to be limited, limited to people that will be educated in a certain way of thinking that will certainly give interpretations that is part of the dogma.
Even in our time there is a part in the bible that says that it can only be interpreted by a certain kind of mindset and that a 'natural man' cannot understand it.
What I am talking about is taking that to a societal level, turning it 'grimdark', adding in 20k years of experience in social engineering and a plan.
One thing that has not happened in the known history of the Amarrians, is civil war.
There has only been the Reclaiming which, according to the history (Scriptures), has always been successful.
There was no civil war when Jamyl was handed the Throne by the Theology Council.
There was no civil war after Vak'Atioth as the Emperor failed the whole Empire.
There was no civil war when Khanid left the Empire.
There was no civil war when Takmahl were driven out of the Empire.
All of the information from the past of the Empire is edited.
Only way to do that in a way that does not threaten the stability of the Empire is by having one institution that gives out the edited information which is needed in the situation that is in the Empire at any current time.
What would have the Emerald City been like if every joe, dick and harry would have had access to the rooms of the Wizard?
Just one girl broke the illusion and destroyed the whole regime.
That is why the Theology Council does not want anyone else to have access to the Scriptures or even the capability to decypher them.
The puppet masters do not want anyone to see behind the smoke and mirrors.