No one looking objectively at Thedosian history can disagree that Andrastianism was founded on war and death. That being said, it was also converted people willingly at the time, too. See Shartan and probably most of Tevinter slaves.
Well, yes. Denying willing converts would be stupid. I will call the Chantry many things, but stupid isn't one of them.
Andraste was obviously a very compelling figure in her time, even moreso after her death. But still, the religion's foundations were in war. A war to end systematic injustices in Tevinter, but still a war. Hessarian's 'convert or die' stance was doubtlessly done for both religious and political reasons. Afterall, a great deal of his population had just seen him kill their messiah, and there was a huge army that still flew her flag. Had he NOT converted, politically he'd be in hot water. Once he did convert, however, he had to be brutal with his enforcement of the new religion. But these were the actions of a ruthless politician, not the Chantry. The Chantry as we know it didn't even exist until Emperor Drakon formed it in -3 Ancient. We can hardly hold his actions over their heads.
Technically, the Orlesian Chantry copied the Tevinter system, added a few tweaks to it, and pretended it had created the Chantry itself.
Because politics. Having the Chantry centered in your country under your rule gives you immense influence. And Drakon had just finished unifying his land by the sword in the name of the Maker, so a little boost in influence and popularity was probably not misplaced.
That begin said, does the current Chantry practice conversion by the sword? Each of the Exalted Marches can be explained away as the Chantry reacting to an outside threat, or having an internal squabble over theology. The last Exalted March ended with the signing of the Llomerryn Accord in 7:84 Storm. The nationalist and minority Chantry forces in Rivain led a massacre in their home country after Qunari converts refused to abide by the treaty and leave for Qunari lands. This was over 150 years ago. In the time since, the Chantry has been under no serious external threat. The Blessed Age was a time of peace for the Chantry(Ferelden, not so much). The current Chantry isn't really set on the conversion of the heretics and heathens. It's more focused on the interests of the church within lands that are already held by Andrastian rulers. But the secular rulers in Andrastian lands seem pretty able to hold their own against the Chantry if they need to. None of them are theocracies.
I have argued, and will continue to argue, that the Chantry was heavily involved in starting the war with the elves. The historical accounts of both sides are filled with gaps until they are put next to eachother. This does not justify the elves in any way, but does show that the Chantry was looking to gain from that war from the very beginning.
The Tevinter marches were much more straightforward: Already suffering from a rather low reputation due to being, well, Tevinter, when they then altered the Chant of Light to reflect better on mages the Chantry had all the excuse they needed to bring the heretics back in line again (nevermind that the Orlesian Chantry rewrote the chant for their own benefit themselves as well).
^ I would stop calling it a golden city, when the thing had been corrupted already by the time Cory's team had gotten their, in the first place. The Blacken City was probably the Eternal city of the Elven Pathon story, as they state in their own lore it was closed off from them by their version of the Loki figure in Norse mythology Fen'Harel. According, too the wiki page their gods are locked in a city in the fade sound familiar? Ie The Blacken City.
And the elven religion does mention four evil Forgotten ones, while the mages found four greater demons, There do seem to be a lot of parallels.
Chantry tradition still says that the Magisters' very presence in the Golden City blackened it. That still applies. Corypheus never saw the Golden City because his presence made it black. This is the Fade we're talking about here. There's no reason to believe that the effects of Magister prescience in such a place didn't blacken it immediately.
We do know that the Black City, the only constant in the Fade, was once Golden. But after the Magisters entered it, it became Black. Something definitely changed when the magisters did what the did.
Edit: Semi ninj'd 
Two problems I have with believing the Chantry version is that, one: none of the Chantry's scholars or members were there and two: the Chantry has already shown it loves to interpret things to their advantage.
We have a first-hand account saying that the city was already black when they arrived, and makes no mention of any 'Maker' casting him out (something which the Chantry does, extensively). Said first-hand account has no reason to lie to us whatsoever. As much of an evil overlord as Corypheus was, I am far more likely to believe his account on the story here.