Maybe a little bit: England and Northern Ireland are Protestant and Ireland proper is Catholic, but, yeah, it wasn't a Holy War outright.

That's actually a good anology because while England doesn't ban Catholic churches in N Ireland (at least I'm pretty sure they don't :\ ) just like it doesn't seem that the Empire is enforcing the ban on Talos.
At the time of the writing of my post I did not think about the Protestant vs Catholic tensions in the UK to be honest, but now that you mention it does fit to a certian extent.
I think he's working under the common misconception that Ulfric Stormcloak is a secret Thalmor agent; but this simply isn't the case. It comes from misinterpreting the Thalmor dossier on him.
It's possible, but there are some of us who think that the Stormcloaks are doing what the Thalmor want them to without taking any orders from the Thalmor. I can only speak for myself, but I think that something akin to the rebellion was what the Thalmor hoped for when they dictated the terms of the peace treay. If the citizens and separatists of the Empire keep killing each other, it leaves less for the Dominion to handle. If I put it this way, let's pretend that there is no recovery after the Great War past the point we are at, and let's simplify it. So we say that the Empire has 10 000 soldiers ready, and the Dominion has 10 000. Then along comes Ulfric, and 5000 of the Imperial troops join the Stormcloaks instead.
Then we have 10 000 Dominion soldiers, 5000 Imperial ones and 5000 stormcloaks. Then we have the civil war itself, and there could be several outcomes but we keep things simple for now, so 4 different endings to the war.
A ) Stormcloaks win a great victory. The Stormcloaks manage to gain independence for Skyrim and has 4000 soldiers left. The Empire only has 1000.
B ) A stalemate is reached, but the Empire agrees to let Skyrim go. Both the Empire and the Stormcloaks have 2500 remaining soldiers each.
C ) Same as B, just that the Stormcloaks concede to defeat. Same number of soldiers, but the Stormcloaks join the Imperial army, Empire ends up with 5000 soldiers.
D ) Empire wins a great victory. Imperials have 4000 soldiers left, plus 1000 surviving Stormcloaks who join the Empire, = 5000 troops.
So, with the Civil War being over, lets look at the odds for the Dominion after all the scenarios.
After outcome A - Dominion has 10 000 soldiers, they now have 2 enemies they can attack separately, independent Skyrim with 4000 soldiers or the Empire with 1000 ready soldiers. 10 000 vs 4000 or 10 000 vs 1000
After outcome B - Dominion has 10 000 soldiers, 2 enemies they can attack separately, Skyrim with 2500 soldiers and the Empire with 2500 soldiers. 10 000 vs 2500 in each war.
After outcome C - Dominion has 10 000 soldiers, only one enemy for the Thalmor, the Empire, fielding 5000 troops. 10 000 vs 5000
After outcome D - Dominion has 10 000 soldiers, Empire has 5000. 10 000 vs 5000
This is oversimplifying things to the extreme, and all the numbers are purely made up, but I figured it was for the best so that everyone could understand it with ease, and it was just to demonstrate how the civil war may benefit the Thalmor.