It's all in how you RP it. Nothing says people are automatically more likely to trust a human noble (depending on where you are on the social ladder and how you've been treated by them, you may be very wary of a noble - think of the City Elf or Dwarf Commoner Origin from DAO.) And I believe there are dialogue choices for a Trev warrior or rogue where you can basically assert you're the youngest of a very minor family. Considering the number of mages, there are a lot of family members of mages running around, and some of them will think "my little brother who was dragged away" rather than "scary demon-loving monster" when mages are brought up. Plus, the Chantry essentially tolerates mages exactly so they can be thrown at the big, world-threatening dangers...like Corypheus. And there are perfectly good reasons for all of the races to be there, though I think they left them a little too vague to allow people to RP the details.
I'm disappointed that your choices don't influence much except whether or not your companions stick by you - there are some choices in-game that I think would put a serious dent in the Inquisition forces and in support for the Inquisition.
Eh. We're talking about the Andrastian masses and the people with power and influence in the Andrastian nations. They're more likely to accept a human Inquisitor, because they are mostly human. Or dirty unwashed elves of no importance. Maybe a tiny handful of Surface Dwarves like Varric. The noble part is less important than the human part. And the Trevelyans aren't the most influential family, but they are large, generally well regarded and Josephine will mention that the Trevelyan's noble status does grant them some influence in Val Royeaux. Not as much as she would have liked, but there's also the implication it's not because the Trevelyans aren't noteworthy enough, but because they are Marchers and thus automatically inferior. She also mentions that one of the Trevelyan's parties were must attends for everyone important in the Free Marches. So they're not an insignificant family.
There actually aren't that many mages running around. Few enough to fit into 15 Circles across all the Andrastian nations. And their relations are just as likely to think "my little brother who accidentally burned the whole house down when he had a nightmare" or if you're Meredith "My beloved sister who wasn't dragged away and then turned into an abomination and slaughtered my entire village including our family". Fear and distrust of mages isn't solely out of the belief they are all evil monsters. Just that they're dangerous, sometimes even when they don't want to be. That's an attitude that was prevelent even before Kirkwall, the attempted assassination of the Divine by a blood mage, the Mage-Templar war ravaging the countryside and of course the actual death of the Divine by magic and of course the creation of a gigantic hole in the sky that spits out demons.
Anyway, I firmly believe a mage Inquisitor can amass enough goodwill to sway public opinion, especially if you also had mage assistance closing the Breach. I just think they should garner a lot more distrust by default.
The only time we really see that reflected in game is at the Winter Palace and even then it's only a tiny bit of Court Approval.
I most definitely agree. In RP respects the Elven, female and Mage aspects create the richest experience in my opinion. As a First you are already being groomed for leadership and have to deal with being a shark out of water as an Elf and Mage. As a Mage you were warned against attracting the attention of Templars by your Keeper and as Dalish Mages are considered Apostates by the Chantry and hunted, albeit not as rigorously, not to mention all the horrible things the Chantry has done to your people. All of this gives you an emotional stake in various themes and choices, more so than other races and classes. There is also more weight added to the decision regarding the Well of Sorrows. Also the Female Elf is the only gender and race that can romance The Dread Wolf himself.
I think Human Inquisitors make the most sense from an in-universe perspective, but Dalish Mage romancing Solas is absolutely my favorite story for all of these reasons. 