Dude, his commander was like "This guy isn't on the list....all well, I'm sure people would like to see an argonian get killed this time."
Quite harsh for just an illegal entry.
You're not on the list because you're the only non-stormcloak on the wagon. Jiubs 1-5 are stormcloak footsoldiers, Jiub 6 is a mid-rank stormcloak, and Jiub 7 if Ulfric Stormcloak. They were all captured in some heroic raid deep into Stormcloak territory, and their names were written down on a list so the empire could do a Roman style embarrassing execution. You were picked up along the way, and since you weren't a stormcloak, you were just slotted for a regular-style execution.
Now, if you ask around, a lot of NPCs will tell you that they're recent immigrants. None of them got arrested at all. Immegration isn't the crime you're being charged with, it's illegal border crossing. Nobody knows what it is that made your border crossing illegal. Maybe you were a famous fugitive from the law, and the Nords just had no time for fancy extradition. Maybe you crossed the borders by killing a man and stealing his horse. It's all up to you to imagine.
Now, yeah, it's probably a dike move, and we know that the empire killed a dude just for leaving a door open (opening event after entering Solitude) but still, this isn't completely black and white.
I think that merchant was a High Elf. There's two other Altmer who appear to be doing fine, as well.
So the Altmer can get along with Nordic Great War veterans, but Dunmer can't?
It's all about the style of arrogance. That stallkeeper "knows" she's better than the nords, and is just there to make a profit ripping off all the simple-minded nords. If she has to pretend to respect them, and play along with their silly orders, she'll do it. The dunmer on the other hand...
The racism seems to be more of a Windhelm thing than a Stormcloak thing. I'd imagine Western Skyrim would remain tolerant under Ulfric. Can't say for sure, though. Haven't done the Civil War questline.
Ulfric just doesn't care about foreigners. With him as king, there'd be no persecution of the elves, but there'd also be no protection. If a Khajiit or Dunmer or Bosmer caravan was attacked by bandits, he'd do nothing to help them. Admittadly, I got this impression from the dude who ends up taking Ulfric's throne after you kill him.
If they're bastards, it's because they, as individuals, are.
This is the answer to the OPs question.