If I remember correctly, Civ IV 'no animations' actually still had animations. When you took your stack and attacked, you would see multiple units spread out over one tile, and then they would all be animated when they moved onto the tile you just attacked. You also had animations for general troop movement.
As it stands, Civ V is just a big teleportation fest. If I move a knight 3 tiles, I just see him appear without any movement animation from one tile to the other. That it no way effects the speed of the MP game, with or without animation the time for the unit to appear on the new tile is the same, and BESIDES, CIV IV had movement animations and a few others.
The big thing that cause slow downs in civ iv was the zoomed combat animation and about 5sec wait for each battle to finish. Get rid of combat zoom and it was a nice compromise, it allowed some animations to occur but no combat zoom and battle resolution animations. It was never as bad as Civ V though, where you just teleport and see numbers pop over your head. Hell, Civ V doesn't even show animations for one quick volley of arrows.
And leave the ultra comp guys alone, they have their own issues to work out. If they are unable to see the value in having a server side option that is easily visible before joining the game, let them. We understand why they would want no animations (although the current implementation of what no animations constitutes is obviously not optimal and could be improved - ie, civ iv), so hopefully they can understand why many would like to have the 'OPTION' to have them on.
This game needs the support of the ultra comp and the normal players both, so try to find a way to get along. It's not "YOUR" game, it's "OUR" game. I always thought the Civ community as a whole was more mature then other gaming communities (ie, counter-strike, WoW, l4d...)