Take the Tet Offensive for example. From a purely military perspective it was a total disaster for the NVA. Casualties were incredibly in the favor of the SV and US forces for a fairly small amount of territory gained. What the NVA realized correctly though was the effect that the Tet Offensive would have on an already questioning American public. The media impact of the Tet Offensive along with the request for another 200k recruits did a major blow to the American public who really began to lose faith with the war. The NVA understood that they didn't have to beat the US Army, they just had to make the American public unwilling to fight.
Note that this isn't an argument that the War was worth fighting or not. Simply that protesters can and do have an effect on how the enemy fights and can assist the enemy intentionally or unintentionally. War in the modern era is no longer just calculated in how it affects the battlefield at hand, but also the media landscape. That was one of the major lessons of the Vietnam War.