Between Black Marsh and Morrowind, I think it's a matter of politics more than racial tension, though certainly racial tension may result from those involved. Looking at the conditions beforehand, you have a lot of people, of various races, involved in Imperial affairs. They move out of their home provinces and live life by the empire. These people, whether they are Argonian or Dunmer, could sympathize but they've probably haven't been involved enough with their provinces to truly care. Many Argonians were not slaves and worked peacefully with Dark Elves who weren't slave owners. Like it was said above, I think it's a matter of the An-Xileel attacking Morrowind, but not the Argonians as a people attacking the Dunmer as a people.
Also take note that Skyrim happens 160+ years after all of that.