Racial harmony in Tamriel is possible, yes and I'll tell you why. Let's take a look at Riften. That city is full of Dunmers and Argonians living together and we all know the Argonians waxed the floor with the Dunmers centuries ago in response for centuries of being slaves of the Dunmers. In Riften I NEVER watched a fight between Argonians and Dunmers, just some conversations between Keerava and Indaryn as well as a worried Tythis about his friend Wujeeta. And let's not forget Brand-Shei, A Dunmer who was raised by an Argonian family.
Well, if the Argonians and the Dunmers could put all their past behind and get along with each other (at least on Skyrim), so will the other races. The only problem are factions that incite xenophobia such as the Thalmor and most of Stormcloaks supporters.
The Dunmer would have to compensate both the Khajiit and the Argonian Races for their enslavement, Ulfric and his nationalist cause would need to be given fair voice at the Elder Council in Cyrodill (a bit like the Scottish and Welsh Assembly's) to end the Civil war, a more lasting peace then brokered with the Thalmor with regard to religious freedoms within the White Gold Concordant, the Dominion to withdraw from Skyrim all together once these protocols are in place I believe relations between all would definitely improve somewhat.