I think Andrastians would logically care. If the Inquisitor is non-human and non-Andrastian, than the leader of a growing military group that aims to spread across Thedas (in the wake of the veil tears) is a potential heathen (and possibly a mage if the main character is either Vashoth or Dalish). Wouldn't the religious leaders of the Andrastian Chantry care that a heathen is growing political and military power? Wouldn't one of the templar factions care that a free mage is in a leadership position over non-mages?
For them not to care would be a bit silly. The humans of the Andrastian kingdoms will see a Qunari with a Vashoth protagonist (since it's doubtful most of them can tell the difference from appearance alone), or one of the People with a Dalish Inquisitor (who is likely going to be a mage, making the elven character a maleficar for practicing non-Circle sanctioned magic). I think, realistically, they should care.
Well lets see- Demons falling from the sky, general chaos broken out, large portions of leadership in The Chantry, Templar Order, and Mages being wiped out in a disaster of some sort, Open Rebellion in several countries, "Human sacrifice, dogs and cats living together... mass hysteria", in other words people are a little more concerned about staying alive than they are some of their petty racial discords. Which if you view things historically there are quite a few examples of groups with extreme culture or dogmatic differences banding together for mutual survival.
Plus, there is that image that most people believe is the Divine annointing the PC as Inquisitor.
So while there will be issues, I don't think that just because someone is Andrastrian, means they are automatically going to be a total non human hating non adrastrian hating piece of trash. Heck they didn't even kill Sten outright when he murdered people in DAO and he is both non human and a religion that is exremely anti Andrastrian.
Oh yeah, DROP THE FRICKIN MERRIL DEBATE, THE HORSE IS DEAD, DECOMPOSED, REINCARNATED, DEAD AGAIN, AND PROBABLY FOSSILIZED BY NOW!