As much as I dislike the WWII comparisons, here's one that's particularly apt.
Imagine the Sunnis and Shia are the Germans and Russians. Even though we were fighting Germany, would it have been in our interest to withdraw from Europe after landing at Normandy, and let Stalin wipe out the Nazis for us, all the way to France? Al-Sadr is no more our friend than Uncle Joe was, common enemy or not.
If that's their reasoning for supporting the Madhi Army, then they need their heads examined.
Whoops! Forget my follow up comments. I failed to properly read your comment to jmc1969. Obviously what I wrote simply echo your analogy.