The government of South Vietnam was screwed up, alienated the majority Buddhist population in favor of the minority Catholic population. Hard to win “Hearts and Minds” in that environment.
Some people turn that around and say that at least Diem had some authority and when he was killed we really lost a chance to win. Hard to know what to do under those circumstances.
I didn't find the series sympathetic to North Vietnam or the Viet Cong. The focus was more that with enemies determined to lose millions of lives there was no way we could have won (without utterly destroying the country and our own reputation).
This was the argument used by liberals against maintaining support for South Vietnamese president Ngo Dinh Diem. However, after he was overthrown and murdered in 1963, I don't believe any of his successors were Roman Catholic.
in the end, the South Vietnamese didn't lose because they failed to win hearts and minds. They lost because they ran out of ammunition thanks to a niggardly Democrat-run Congress.