Strange title, but it comes to this:
During the time, the USA was involved in WWII, Americans seemed to me much more united. Young men were eager to join the army, there was a war-based economy; everything was focused to contribute to the war. During the war in Vietnam this wasn't the case.
But in the late 30's, 1940 and 1941, there was also a large anti-war movement in the USA. If I recall corectely, Henry Ford and Carles Lindbergh were part of the America First movement, which didn't want American interference in Europe. Also there were right-winged organisations who were at least not negative against (certain) fascist ideas.
In the 50's and 60's (large part of) America was (fanatically) anti-communist (McCarthy, Red Scare, etc.)
So how come despite this, people were much more opposed to the war in Vietnam? Was it a difference in generation (soldiers in WWII grew up during the Great Depression, Vietnam-era soldiers grew up during the booming 50's and 60's), was it because the war in Vietnam was televised? Or was it simply more black vs white? In WWII, the USA was attacked by the Axis, while in Vietnam the USA striked first?
There are some huge differences so I would argue this is really an apples to oranges comparison anyway.
First of all, it wasn't until the US was attacked that the war had broad public support. There's no reason to suspect that if Vietnam had attacked the United States there wouldn't have been a similar level of popular support. In fact, the government still felt that it had to justify the large scale escalation of the Vietnam War on the basis of a supposed attack on US forces by the North.
Secondly, the idea that there was no dissent against WWII is a bit of a myth. There was an overwhelmingly broad consensus in support of the war by comparison to Vietnam but it wasn't universal.
I would say that your answer lies in the reasons that Vietnam did not gain support rather than having anything to do with World War II itself. But in summary, Vietnam didn't represent an obvious vital American interest, it was broadcast into the living rooms of the American public every evening, and it did not appear to be a war that the United States was winning decisively (or at the very least the government struggled to communicate the successes in a way that the public could understand).
Americans generally don't want to support wars that have no clear objectives, are costing vast sums of money and thousands of lives, and are being run by politicians which are not clear about their political and military goals. Plus it was the first TV war. The only strong similarity WWII shares is the cost in lives and money but the goals were concrete and the press was much more effectively controlled so hard questions didn't tend to enter the public discourse in the same way.