Was there any racism or prejudice from other American troops due to them being the same ethnicity as the enemy? Did they also experience some culture shock going to their native country probably for the first time?
Unlike today, circa 1965 there were probably few, if any Vietnamese Americans in the US military. Unlike Chinese, Japanese, or Filipinos, there was not a sizable population of Vietnamese living in the United States in the years before the Vietnam War.
The large number of Vietnamese living in the United States, Australia, France, etc today are a product of the Indochinese refugee crisis that followed the defeat of South Vietnam in 1975.
In the broadest terms, there were three waves of Vietnamese immigration out of Vietnam. That was prompted by those fleeing conditions in Vietnam (due to the disastrous economic collectivization policies of the Socialist Republic of Vietnam the went on from 1975 through the mid 1980s), and those persecuted for their connection to the South Vietnamese government or military (hundreds of thousands of whom were held for 're-education' in concentration camps after 1975). Those migrations lasted into the late 1990s.