From what I've read, Varric usually seems to be well-liked by most people. I honestly don't think I've personally read anyone saying that he's not a real dwarf, so I can't comment on that. He's typically one of those characters most groups agree on even when they hardly agree on anything (like mages or templars). I even recall a fan faux cry over the "bearded Varric" mod.
I probably shouldn't have used Varric as an example, because he is very popular and charismatic. It's more about surface dwarves in general and those that reject traditional dwarven culture. "You might as well be playing a short human" was a common line when Cadash was announced as a surface dwarf. And I love traditional dwarven culture (from a storytelling standpoint. I wouldn't want to live there!), but acting like a dwarf isn't a dwarf because they don't represent it strikes me as misguided.
As for elves, I usually read plenty of people on tumblr saying they all get a raw deal. The lack of real rights, the purges, the standard view of them as "less than people" - they were dealt a very bad hand.
I've seen that, too. But I've also seen the other thing, discrediting their point of view.
Heck, Celene burning down Halamshiral is usually the number one criticism against Celene I've read about, typically along with her treatment of Briala (murdering her parents and fetishizing her).
Definitely true. I was horrified when I read that and I hope that most people find her actions abhorrent.
Sera doesn't like elves, so that's why she gets brought up in certain discussions, but that's usually discussions about a pro-elven companion missing from Inquisition.
Sera not liking elven culture gets brought up whether it's relevant or not. It's frustrating. Where's the pro-Vashoth character in the face of Bull's bias? Where's the traditionalist dwarf to contrast Varric? These games espouse a lot of viewpoints, but every game is not going to express every viewpoint.
I guess we just see different things. When I think of what people have said about those characters, I'm reminded of the 'three elven advisors' pitch a fan did involving Zevran, Merill, and a coffee drinking Fenris who was sick and tired of everyone's ****.
Like I said, I see that stuff too. Plenty of people don't dismiss their experiences, I'm just saying that there are people who do.