Technically you can be an Andrastrian and not support the Chantry and their interpretation of the Chant. Anders was an Andrastrian, so was my Hawke and I even argued a case with Sebastian that Andraste would have have been there alongside us defending the innocent mages from being slaughtered for something they didn't do. Since I had killed Anders he was willing to concede on the matter.
The first time I played Origins it was as a Dalish elf. I was incensed when I discovered the Chant had been altered to remove the sections about Shartan. Then I was pleased that Shartan appeared among the spirits at the Gauntlet, which made me feel that what I was told there was at least genuine. The more honest Chantry scholars admit that Andraste's crusade might well have foundered but for Shartan turning on his masters with his elven soldiers and supporting the barbarians at the Battle of Valarian Fields.
Sebastian also had a chat with Merrill when he suggested that when he talked about the Maker rejecting humanity and she talked about the Creators abandoning the elves, perhaps they were talking about the same divine force. So you could work to that basis, so even if the dialogue makes you refer to Creators, effectively you are saying the Maker.
On the whole though, the PC is never actually made to subscribe to a faith. You can accept the blessing of the cleric at Ostagar or reject it or simply avoid her altogether. Likewise you can ask Elthina for her blessing but it is not obligatory. I think in this game you can devote resources to building a local chantry at your Keeps if you wish but again it is your choice. I want to be able to promote the real chant (in other words the true morality it promotes not the pseudo version of the Orlesian Chantry) but I am not sure if that is possible. Remember that Tevinter is also Andrastrian, but has broken away from the Orlesian Chantry and put their own interpretation on the chant.
Strangely enough, at the time of the original Inquisition there were a lot of different cults all devote to Andraste but that organisation thinned them out until the one remained that they approved of, which also happened to be the one favoured by Emperor Drakon and so the Orlesian Chantry and the Divine came into being.