Actually, lots were against the way it was prosecuted by the at-the-time-Liar-In-Chief, LBJ.
(Seems LBJ also taught Clinton a few things about how to handle politically-damaging people, BTW)
Unfortunately, the real reason for the protests--LBJ/MacNamara's complete disregard for the US military man--was over-ridden by the pure anti-US crowd.
There were, and ARE, such people as "honest" protesters.
For example, in Iraq--rather than suffer continuous guerilla attacks, why doesn't GWB simply order the new MOAB to touch pavement in Tikrit?
Because that's not the way to reach the hearts and minds of the Iraqis and other Arabs wo might be inclined to support us. The Russians completely flattened Grozny but it didn't stop their problems in Chechnya. It just made the Chechens thirst for revenge.