Yes, but I'd hope simple geography is everyone's friend, post-Cold War. The West is American, the East is Russian, Muslim, and Oriental. Who would want to upset that balance?
As in WWII.
Nevertheless, clearly, there is room for common purposes for entirely different reasons, and it behooves the U.S. to continue doing what is in the best interests of The U.S. also.
The U.S. is no exception to the reality that nations do not have friends, cannot; just national interests, which must change from time to time.
I said it early on, that a no-rules commitment by the U.S. and Russia to work together to eliminate al-Qaeda (or any other terrorist group) cannot fail. In the long long more lives might have been saved, on all sides, had this been done overtly a lot sooner.