While it's not clearly defined as such in its description, I've always assumed the spirit of Eskimos Aren't Real is "character doesn't believe in something comically mundane that's obviously real", whenever that be Eskimos, or the nation of Sweden, or the Queen of England. Not quite sure about the differences between Arbitrary Skepticism and Flat-Earth Atheist, but I've usually perceived those two as usually applying to fantastic subjects, or more broadly anything that doesn't exist in real life.
The difference between Arbitrary Skepticism and Flat-Earth Atheist is proof. The Flat-Earth Atheist has it (or at least could easily acquire it), but ignores it. Arbitrary Skepticism doesn't require it. Imagine someone in a world where most people believe magic is real. This person hangs around with wizards all the time, and knows that they're a thing. However, when the possibility of ghost is brought up, they dismiss it out of hand. That's Arbitrary Skepticism. Now, if they then meet a whole bunch of ghosts, but still claim that there's no such thing as ghosts, then they're a Flat-Earth Atheist. If anything, Flat-Earth Atheist is the most similar of these tropes to Eskimos Aren't Real, as it is essentially Eskimos Aren't Real, but for fantastic elements.
As far as I can tell, you're right about everything else.
Bigotry will NEVER be welcome on TV Tropes.

So, Eskimos Aren't Real has been looked over by the Tropes with Outdated and Offensive Names
thread for its first word. That thread (unfortunately) doesn't have the authority to change names on their own, so it needs a Wick Check to go through TRS, but there was enough concerns that the name was misleading people into thinking that it was only for people not believing in the existence of specific real ethnic groups while the trope covers much more ground. That's what I started Wick Checks Arent Real to look for. But then I slowly realized that we already have quite a number of "disbelief" and "skeptic" tropes. A lot of these may have issues, and there's a chance a good number of them may not be necessary. So, in the absence of any (finished) wick checks on tropes besides Eskimos Aren't Real:
So, I just wanted to clear some definitions up before I take Eskimos Aren't Real to TRS soon - remember, that still needs a name change if we do decide to keep it. And actually, the trope I'm actually worried EAR is closest to is actually Global Ignorance (which isn't a "disbelief" trope normally, but might eat up a lot of EAR if we decide to split it.) I feel like EAR isn't an entirely necessary trope (even if it got a name change), but I wouldn't want to throw any EAR bullets into a trope that shouldn't be taking them.