Hey there!
Many, especially students at their schools and colleges, during the time of the War. They felt it went against democratic principles.
Let's rule out our other options.
First of all, communism is ruled out. the United States does not support communism and never has. That's usually why we get involved into global affairs we have no place in-- because the United States always makes efforts to preserve democracy and forbid the spread of communism.
Next, they didn't think this because there was a war going on. People knew better than to have the largest, nuclear-armed, superpowers in the entire world fighting. That's perhaps why the cold war was more tension than actual fighting. Nobody wanted to get engaged into nuclear war.
Lastly, the US was being aggressive enough, and part of the reason they protested was to limit the violence, The US already deployed harmful things such as Agent Orange and traditional Vietnam traps, and nobody wanted more of that.
Hope this helps!