As the flair states, a very interesting question. It is especially interesting since we rarely hear the Vietnamese voices in the historical narrative. The South Vietnamese narrative is also one that tends to get lost in the din of the Vietnam War historiography. What we find when we look at the anti-war movements in the respective countries we find some interesting nuggets of information. First, we find very little information about South Vietnamese views on the US anti-war movement. What is ironic about this is that US presence in the Republic of Vietnam was intrinsically tied to every day life. We can, however, draw inferences from the available resources we have. The clearest views are those of the government officials directing the war. We can see some anxiety expressed by the Thieu/Ky administration in South Vietnam. In a report on a conversation between Nguyen Van Thieu and Richard Nixon (plus various state department officials) the American anti-war movement is noted multiple times. In particular the anti-war movement is noted as a strategic threat to the war effort. Second, we must see the anti-war movement in South Vietnam and its similarities to the American anti-war movement. This is crucial to understanding the mindset of Southern peoples and especially the youth.
Nguyen Van Thieu and Richard Nixon
On July 30, 1969, Richard Nixon, Henry Kissinger, and Nguyen Van Thien would meet with other officials to discuss the progress of the war in Vietnam. Richard Nixon's term was not even a year old and needed to be appraised of the situation. Thieu is very anxious for a favorable conclusion to the Paris peace accords. It was these accords that would see the end or preservation of the Republic of Vietnam. Thieu had to have worried about pressures Nixon was facing at home to bring about the war's end. In this document we see the Vietnamese view of the anti-war movement come out most clearly. In later memos we see the anti-war movement in the US crop up as a strategic threat. It was agreed by both sides that the North Vietnamese would see them as a destabilizing force in the US and sought to inflame that force by any means at their disposal. It was a plank in the Northern strategy that they would seek to grind down the American will to win the war. Presidents Thieu and Nixon were very well aware of this. Both men wanted to see the movement quelled for different reasons. For Thieu the possibility of Americans withdrawing from the war spelled the doom of his regime and the end of an independent South. Nixon very much needed a way to "honorably" end the war. It tends to be the opinion of South Vietnamese officials that the anti-war movement was part of an existential threat to South Vietnam itself.
Citizen Views
The views of the average citizen are much harder to discern. There is a lack of secondary sources that directly refer to Vietnamese views on the US anti war movement. However, we can draw strong inferences from the reliance of the people on American presence (especially their money) in South Vietnam. We can see the disappointment that the average Vietnamese citizen had, especially soldiers, at the eventual American withdrawal. In particular I will reference a C-SPAN panel of former South Vietnamese soldiers and officials. We first hear disappointment in the voice of Gary Minh Tran, a former Southern cabinet member. He said in the last year of the war the Southern people felt very disheartened and abandoned by the United States. The lack of logistical support was starting to throttle the South Vietnamese war machine. While cash continued to flow in from China and the Soviet Union to the North, the South Vietnamese were cut off. Minh Tran goes on further to state that the general feeling was that the manpower was there, the will was there, but US withdrawal was incredibly damaging to morale. It was particularly harmful since the US had promised continued support even after withdrawal in 1973. This was a promise that congress would not fulfill.
Another important perspective to consider is the view from the South Vietnamese that they were fighting a civil war. Though, this view was not shared among the entire citizenry. We see particularly vocal anti-war groups within the student population. Some saw the war as one of an invading foreign force. We could further imply that depending on your view of the nature of the conflict there would be radically different responses to American anti-war efforts. We saw previously that the North Vietnamese saw anti-war sentiments at home as a potential gain for their own strategic goals. Students in the South had known nothing but war, ever since the mid 1940s Vietnam had been embroiled in civil conflict. Stress and anxiety were high among the youth population of South Vietnam especially. There was not only the ever present threat of violence but the draft loomed over the heads of many Southerners. Many student groups became increasingly vocal as the US presence in Vietnam began to ramp up after 1965. The further we get into the war the more radical youth opposition to the war would grow.
Why don't we see more direct references to the US anti-war movement in particular? This comes in part from major suppression of the freedom of association and discussion. The government of South Vietnam for many years had been plagued by corruption and accusations of civil rights abuses. The first major repressions came against Buddhist anti-war movements. When student groups spoke out in their defense we see a wave of arrests sweep campuses. We will also see a number of extra-judicial killings that sought to control the narrative. The flow of information into the country was also heavily regulated by both US and Southern officials. It was in the best interest of the US not to allow any more fuel to fall on the anti-war fire. Richard Nixon had been barely able to quell anti-war fervor after it reached its fever pitch in 1969. Having the Vietnamese further inspired by acts back home would have proved disastrous. However, in 1970 Saigon students would riot in the streets after an expansion of the war into Cambodia. Similar protests would be mirrored in the US. Whether the two are linked is unclear, but the motivations are likely the same. In footage provided by the AP we can see the phrase "Stop War Immediately" scrawled on a student banner. With Northern infiltrators in many of these groups, it is very likely that they were inspired by American students (As North Vietnamese officials kept a close pulse on public sentiments in the US.)
I hope some of this answered your question.
Source List:
"The Vietnam War" By Ken Burns and Lynn Novick
Nguyen-Marshall, Van. "Student Activism in Time of War: Youth in the Republic of Vietnam, 1960s–1970s." Journal of Vietnamese Studies 10, no. 2 (2015): 43-81. doi:10.1525/vs.2015.10.2.43.
Dror, Olga. "Raising Vietnamese: War and Youth in the South in the Early 1970s." Journal of Southeast Asian Studies 44, no. 1 (2013): 74-99. http://www.jstor.org/stable/23321691.