The major effect that foreign policy had on domestic policy during this time was that the Vietnam War took huge amounts of money to fight. When added to the price of President Johnson's Great Society programs, these expenditures helped lead to financial problems for the US in the 1970s.
Domestic policy also impacted foreign policy. The Democratic Party needed to look like it was strongly anti-communist because Democrats were typically seen as weaker on that issue. In part because of this domestic political need, the US got further and further into the war in Vietnam.