Power resides in balancing off potential enemies one against the other.
During Britain's heyday the European "balance of power" was the foreign policy goal, achieved by helping the weaker party of a dispute against the stronger. With the French Revolution and Napoleon this balance was hard to restore, and cost much British treasure and life (though it was much more costly for the Russians, Germans, and Austrians).
Napoleon III later allowed Prussian hegemony in Central Europe, destroying the careful balance of power built at the Congress of Vienna. This lead inexorably to WWI.
In all fairness Napoleon III had his hands full with domestic issues, but he sure was dumb in foreign policy.
Nixon's Chinese foreign policy forced the same "balance of power" logic on the Marxist-Leninist countries, making the United States tremendously more powerful versus the now divided Communist world.
The Soviet Union had been threatening China with full bore nuclear war, making China willing to negotiate with the Capitalists. Dumb, that.
"The more things change the more things remain the same."
Countries have interests, not friends.
Russia has no interest in helping the U.S. remove the mullahs from power. The opposite is true.