Well, maybe the paranoid leaders of the Dales shouldn't have cut a swath of death and destruction through Orlais because the Chantry was sending Templar bodyguards for their missionaries who were being religiously censored. 
Actually, it read that templars were sent into the Dales as a consequence of kicking out the missionaries and refusing to convert, not that templars accompanied missionaries.
Templars are the militant arm of the Chantry, as their own codex attests to: "Often portrayed as stoic and grim, the Order of Templars was created as the martial arm of the Chantry." Their faith in the Maker is also a primary issue for recruitment, according to their own codex: "In reality, the Chantry's militant arm looks first for skilled warriors with unshakable faith in the Maker, with a flawless moral center as a secondary concern. Templars must carry out their duty with an emotional distance, and the Order of Templars prefers soldiers with religious fervor and absolute loyalty over paragons of virtue who might question orders when it comes time to make difficult choices."
Sending armed and armored soldiers - the militant arm of the Chantry - into a region with followers of a different faith and free mages was certain to cause problems, particularly when the templars view themselves as having "dominion over mages by divine right". It's the reason why the elven Warden can outright condemn the Chantry for invading the Dales because the elves wouldn't convert.
The least they can do for the people who follow the religion of the woman who freed them from enslavement is to let their missionaries wander around and talk. They don't have to listen if they don't want, but kicking them out and who knows what else to the point the Templars have to serve as bodyguards is messed up.
Andraste and Shartan fought Tevinter, with the support of the humans and elves who committed to their cause to battle the Imperium. That's something people often forget in these discussions. A dream of an elven homeland is even mentioned by the apparition of Shartan in the temple, “It was my dream for the People to have a home of their own, where we would have no masters but ourselves."
Also, considering Kordillus Drakon I lead a series of Exalted Marches to conquer his neighbors and establish the Orlesian Empire, the apprehension of the elves is completely understandable. As Brother Genitivi wrote, "Such was the power of the Maker's word that the young King Drakon undertook a series of Exalted Marches meant to unite the city-states and create an empire solely dedicated to the Maker's will. The Orlesian Empire became the seat of the Chantry's power, the Grand Cathedral in Val Royeaux the source of the movement that birthed the organized Chantry as we know it today."
In fact, Drakon's desired conquest of the Free Marches was prevented due to his issues with the neighboring Dales, which is precisely the reason he turned to using missionaries. This is another issue you seem to have forgotten in your condemnation of the Dalish in the Dales. Kicking out the missionaries didn't warrant an invasion, if the Dalish historical account is correct.
The elves have the right to follow their own religion, and they shouldn't have to capitulate to human demands to follow the Chantry, then or now. An ideal outcome for an independent Dales would be that the elves wouldn't have to adhere to following the Andrastian faith if they don't want to.