Maybe during the Vietnam War, to the effect: Hey, you're assuming that we're preventing greater harm, when in fact we're not all sure of that. And you're assuming that communism is a uniquely bad outcome, when in point of fact there are plenty of things in the world approximately just as bad.
Existentialism might have added a whole new strain of anti-war activism.
And to a large extent, anti-war activists in the U.S. were viewed as immature young people, who just selfishly objected to paying the current cost, and who seemingly couldn't see past their own noses that we were trying to prevent a greater harm. Of course, this wasn't true. There was plenty of older people in the anti-war movement, perhaps most notable Catholics, but plenty of other older people as well. And of course, the idealism of the young should not be so readily dismissed. Young persons often think very clearly and see through much of the hypocrisy we as older persons have gotten used to.
We can perhaps date the time the anti-war movement went mainstream in the U.S. as when Martin Luther King, Jr., gave his speech "Beyond Vietnam: A Time to Break Silence" at the Riverside Church, New York City, on April 4, 1967. And yes, this was exactly one year before his tragic assassination. Maybe if existentialism had gotten some major traction in the United States—and people do like exploring new ideas—maybe this level of activism would have been present one year earlier in April '66. And then we can talk about what kind of difference this would have made.