Obviously the game is about the demonic invasion and the Breach. However, I do hope that we do not have to play by any existing organization's rules or kowtow to them...
I would very much like to tell the Chantry to sod off and that the Inquisition will do things their own way, should the Chantry want to have a say, as well as limit their influence on Theodosian society.
Originally they said we were forming the inquisition in opposition to the Chantry and they have stated that we don't have to support them.
Here is my take on it (which does involves some speculation.
The Inquisition wasn't originally part of the Chantry but they did eventually join with them creating the Seekers, Templar order and the circles. So now we know that reforming it was Justinia's idea, it was a sort of plan b. We also know that she ended up carrying out that plan as that is actually what Cassandra and Leliana were part of in DA2.
Now Justinia is head of the Chantry but she doesn't always seem to have the same views as the majority of the Chantry and she did allot of things secretly. So this group may not have actually been under her control officially.
Anyway it wont be officially or unofficially by the beginning of the game. Our PC has the ability to close veil tears and is also apparently seen as a sort of prophet of the maker (or something) by many. This is why we are the Inquisitor and it also means that we can't really be overthrown. The Inquisition needs our PC to close the tears and as it's figurehead so people like Cassandra, Leliana and Cullen will have to put up with our decisions or leave.
So I really don't think we will be forced to support the Chantry or do as they say.