Not missing the point at all. What I'm saying is where are the schisms between those who believe, and ignore all the Chantry teaching on the matter, and those who don't? They exist for a short time at the beginning and then disappear. The fact that there were schisms in the real life church when you have a tradition of people who do have genuine visions/miracles attributed to them, is all the more reason why you would think there would be much more of a problem in an organisation where they have no tradition of them. The people who refused to tow the line when the church pronounced on the matter are the ones that broke away and are the smaller entity. Occasionally the church decides to wait before making a pronouncement because it is not clear cut. When a person is claiming a vision that specifically contradicts the established faith of the church, that is always a good enough reason to think that it is false.
Then as Solas points out it is a deception; after Adamant all the inner Circle know that it is, as do people like Giselle. At this point, according to the Chantry's own teaching about honesty and how the Maker views deceivers, they should be telling people the truth. Yet they continue to encourage you to deceive people. It is quite possible even if you told the ordinary people of Skyhold they would rather not believe the truth but at least you have been honest about it. As for Josephine asking you what she should say to people from outside your forces who want to know what Andraste said to you in the Fade, the answer is clear, it wasn't Andraste, there is no message.
What makes it worse is if you accepted the title of Herald and are actually forgiving people in her name. Again, you have no divine authority to do this and it is a deception. Unlike the real world there is no ambiguity to this. You know what the truth is. A devout human follower of Andraste should actually have more of a problem with this than another race, who probably isn't familiar with their dogma and so may not feel so awkward about doing so.
The thing was, there were lots of different versions of Andrastrianism at the outset, immediately after her death, all with their own traditions, ceremonies and versions of the Chant. Then Drakon decided to "simplify" things and that is why there is only one (or two counting Tevinter). Strangely enough, if the old cult was still at Haven, they might well have seen you as a prophet of the Maker. After all, they thought Andraste had been reborn as a dragon.
The Chantry Mother in Val Royeaux actually says it: "For you to be true, a great many things must be false. And if you are false a great many things must have failed." She also says: "I am left to question all I have been taught".
In the end it is the heretical belief in the false prophet that wins out but this should not have been happening. There should either have been a permanent split between those who believe you are the Herald and those that don't or there at least should have been large numbers of people having a serious crisis of faith. That is what happens when something like this occurs in real life.