I'm trying to find out how U.S. soldiers serving in the Vietnam War were politically affected when on tour/returning.
The simple answer: Yes. Very.
Vietnam Veterans Against the War organized protests- most notably Dewey Canyon III. In 1971, 1100 or so Vietnam vets marched from Lincoln to Arlington in a peaceful display of protest against the war.
I'd like to give a better, more sourced answer rather than a casual note, but you might want to check out a documentary titled "Sir! No Sir!" This documentary deals with some aspects of your question. There's stuff in "Hearts and Minds" too, but that one seems more a product of the antiwar movement of the era.