Exactly. But first, I have to tell it openly - I do not argue about legitimacy of your arguments. And far from bashing your view of the inquisitor's race. All I am trying to do is to justify for myself the ability to play a race other then human.
So, about dwarves. Unfortunately, there is nothing in human history to compare it with. Even if you declare a barbarian cannibal from a cave "holy symbol" of catholic church, that barbarian still will be a human and there COULD be a missioner who made him a catholic. With dwarves it's still more extreme.
I prefer not to compare Thedas to Earth. It only leads to false correlations.
Trading - sure! There can be no doubts. Official visits from dwarven officials? Any time! They are noble folk, they have a king, they have traditions. Or warriors - who can be better? As a warden your DN is equal to the king and the best of the best with a weapon.
Now, religion - is another matter. It's racial, it's private, it's one of the thing separating the culture. And dwarves were never mentioned in andrasten-t-ism, unlike elves, btw, who owe Andraste their freedom and who were even mentioned in the Chant of Light before.
There for I can not see a dwarf as a Herald of Andraste. Or anything bound to the Chantry. Yes, with kossith it's double so - a daemon like creature sent as a holy messenger? Are you kidding me? But when my dwarf (I tried every race, of course, to see for myself) woke up and heard "it's her! It's Herald of Andraste" - from a local folk who should spit on my footsteps for even thinking of representing the most holy figure! - I was immediately disconnected from the story.
But that point of view - the audacity that a "Qunari", a dwarf, or a Dalish elf could be Andraste's Herald - is noted in the story. Some people are super pissed about it (some people are pissed in the Chantry even if you're a human noble non-Mage). The thing about Andraste is that, while she was a real person, a lot of what's said about her is clearly bullshit (since there are multiple stories) and nobody can "prove" the Maker, etc, etc. It's a religion. Based in some very real lore, yes, but a religion. The idea that you "can't" be the Herald of Andraste if not human does come up but also you have a big glowy thing on your hand, you do stabilize the Rifts and keep demons from pouring out on their heads, etc. I do not have trouble believing that many of the common people - in a time of great fear - would not accept any savior who seems to be on "their" side. That doesn't mean they'll suddenly check their racism as much as they'll make exceptions - people do this all the time.
Now, whether you are or aren't the Herald....as far as I can tell, it's never made clear. You learn where the power came from, etc, etc, but you don't know if everything is the Plan of the Maker or not. This is good. You can be a believer or a non-believer, an Andrastian, a convert, or a believer of something else, or of nothing at all. The story wraps nicely around different kinds of beliefs.
Again, this is the problem - that guy can not be alone. Yet, he is. And at the same time, should there be more of them - game would be unplayable. I am screwed
My point about that guy is pointing out that the Inquisitor (like Wardens, actually) gets elevated beyond race. BECAUSE of what she/he is. If you can close a massive sky rift that would endanger all Thedas, people aren't going to care if you're short or have horns or whatever. I mean some are. (And some do.) But mostly nobles with their heads up their asses - and most of the people you see are commoners. They want things like food, their family's safety, comfort, etc. The whole reason they're racist is likely to make their own lives more comfortable (it puts someone below them in society and it means they don't have to deal with the scary idea of "different.").
I still don't think that applies to dwarves much. Humans don't seem to have much issue with surfacer dwarves and seem to get along with them just fine. They don't want to inter-marry or whatever, or give them too much control, but they're perfectly happy to associate with them. We don't see Varric experience much racism at all, for instance. Now, the church does exclude him - Cassandra says this when she points out he actually believes, but whether it has to do with dwarfyness I can't say - and the church excludes dwarves from service (Mother Giselle says). But that doesn't really say much about the beliefs of the commoners.
Anyway, maybe this helps you play the other races; maybe it doesn't. To me, since it is "reacted" to, I am fine with it. I can easily believe that someone who can close holes in the sky would get a different kind of treatment.