The Empire is a chain. A chain keeping the AD from taking over the world. If one link in the chain breaks, the chain is worthless.
I.E. Without Skyrim, AD wins, Empire loses.
That's funny, since the empire has already lost most of its links.
To the OP: When does Ulfric ever demonstrate "extreme hatred" towards races other than Nords? I'll make it easy- never. The Dunmer were allowed to take Nord land free without compensation, and to swear no fealty to any jarl and remain sovereign. Now they [censored] about it as if that is discrimination. Undoubtedly some Nords do discriminate against them, but Ulfric is simply allocating scarce resources to the war effort and to his political base. He has no obligation to the Dunmer, as they have none to him. He won't let Argonians into the city, but this could be about their reputation as smugglers and thieves, just as the Khajiit caravans are kept out of every Nord city. It may also be to prevent unrest with the Dunmer since those two hate each other.
About your friend's reasoning, keeping the empire together is only a good strategic goal if the empire has good leadership. It doesn't. Cyrodiil is selling out its provinces to save itself and Skyrim doesn't have to stand by and wait to be the next Hammerfell.