Correct, they shouldn't for they don't have the right to do so. The Ashlands will be fine without any "special" knowledge. It's easy to see how you're the bringer of truth when you know the money of the provinces is flowing out of them straight into imperialist pockets. Believe what you want while you're in that City, but it gets problematic the instance you decide believing it yourself doesn't suffice anymore and you must push it down our throats as if our values aren't true enough. The Ashlands have no desire of sending an army out of the wastes to force their customs on you imperialists unlike yourselves!
Once again, truth can be quite relative. There are many things we cannot see or do not understand because we only look at it one way and we think it's the only and right way so far, so much better than the different types of perception that may have been or are still existant on Nirn.
I can't see how the Dunmer who came too much into contact with the imperialists kept their own identity. They became a league of their own, a whole house turned away and all so they could share in imperialist riches, allowed them to build forts, shrines and other foreign buildings that never belonged, but the Ashlanders know there are greater and less shallow things in life. I experienced myself [out of debate: in case you didn't know, I'm trying to debate in persona here xD massive lulz] as a Dunmer how they would call me N'wah for carrying that bit of imperialist flavour in the way I looked, walked and spoke and I never even liked them outlanders. How can you call a Dunmer swimming in septims, wearing Cyrodiilic linen, speaking foreign tongues, praying to false gods still a true Vvardenfellic tribesman? This is unacceptable.
You don't know that the Ashlanders wouldn't cultivate ambitions of conquest. Just because they don't have the power doesn't mean they wouldn't. Dagoth Ur CERTAINLY would've conquered all of Tamriel itself were it not for the intervention of the Empire. And the Great Houses of Morrowind, if given the power, would likely have done the same.
What's the difference between the Empire and the rest? The Tribunal stole divine power and persecute those who know the truth. The Great Houses are corrupt, support slavery and have nothing but hatred for non Dunmer. The Sixth House is insane, monstrous and certainly evil. And the Ashlanders, while perhaps the best of all of them, recognize the outside world but choose not to adapt to it. The world isn't going to grind to a halt for them.
Lets take your example for a moment. Why is that unacceptable? Shouldn't that be HIS choice? And the Nine are not false, even the Ashlanders recognize this. They just do not think them worthy of worship. If any gods are false, its the Tribunal. And yes, perhaps so much change constitutes a change of identity, but like I said, that's his choice.
Now let's take other examples. Look at the city of Tel Vos, and its Telvanni leader, Master Aryon. He is a very open minded individual, and that's saying something for a member of a Great House other than Hlaalu. And yet he retains the traditional style of Telvanni architecture with Imperial indulgence. That right there is your proof.