This is a perhaps unexpected answer to your question but an excellent book on the topic is Jeremi Suri's Power and Protest in which he argues that the social turmoil throughout the world in the late sixties, including the antiwar protests in the United States led to the growing detente between the Cold War Powers in an attempt to create domestic stability. There is fairly good evidence that the two are linked in Kissinger's mind if you read is crazy long "The White House Years." It really quite similar to the way we think of the Congress of Vienna in of 1815 in which the statesmen of Europe arranged a balance of power in order to quell the liberal tendencies brought about by the French Revolution (and exported during the Napoleonic Wars). Which was ... wait for it ... the topic of Henry Kissinger's doctoral dissertation.

The standard answer to your question by revisionist historians of the Vietnam War by the way is to say that the antiwar movements can be blamed for sapping moral and losing the war. The old stabbed in the back narrative. Most historians and I don't buy that.

P.S. Suri's work goes downhill after that book.