There is currently some fear about returning ISIS fighters, and then thought about past wars. Were Vietnamese people allowed into the States after the Vietnam War? How about Germans etc.

There were multiple phases of Vietnamese refugee resettlement.

1 - Government, military, and civil servants (1975)

Operation Frequent Wind was the first large scale resettlement of South Vietnamese refugees—those evacuated consisted largely of government employees, bureaucrats, and higher ranking military officials. Those able to get spaces on U.S. military helicopters and aircraft had to be high enough stature in order to get out of the country (which had technically halted the exit visas required to leave in the final days of the war).

However, during the fall of Saigon, many lower ranking soldiers and civilians commandeered their own craft, both helicopters and watercraft, to escape the final communist push on Saigon. This first wave of refugees were generally considered to have the closest ties to the Saigon government, and thus they and their families were at the highest risk for reprisals from the communists. The Vietnam Humanitarian Assistance and Evacuation Act of 1975 was largely aimed at allowing these people to settle in the United States.

2 - The boat people (the late 1970s - late 1980s)

One of the largest refugee crises of the 20th century, the Vietnamese (and Cambodian and Lao) boat people fled the country for a multitude of reasons. Many of these Vietnamese people were of ethnic Chinese descent—the Hoa people—and many of these people were merchants, landowners, and those generally considered by the communists to be capitalists and the "bourgeoisie." Many had their land and property seized following the fall of Saigon and were forcibly resettled to the New Economic Zones—remote jungle and mountainous regions where these people were forced to work the land. Many of the boat people could be considered economic migrants, though many had the stigma of having worked for the South Vietnamese government or military, and therefore were not allowed to work anything but menial jobs if at all by the new government. Furthermore many of their families were denied entry into schools and thus their economic futures in Vietnam were limited, hence the exodus. The Orderly Departure Program run by UNHCR largely resettled these people, with the United States taking in the majority.

Importantly, public sentiment towards the South Vietnamese refugees was not at all totally positive. In 1979, most Americans opposed the resettlement of Indochinese refugees. Famously, some politicians that you might recognize today, like Joe Biden and Jerry Brown opposed Vietnamese refugee resettlement, with Brown even using some rhetoric that we may hear about refugee resettlement today.

3 - Political prisoners (1980s)

By the late 1980's, the ODP was drawing to a close. Many of the countries with refugee camps in Southeast Asia, such as Malaysia, were beginning to refuse the arrival of more boat people (though many countries were notorious for turning away boat people throughout the decade). By the late 1980s, those South Vietnamese individuals associated with the old regime (who had missed the initial evacuation and thus were sentenced to long terms in the brutal Reeducation Camps) were being released. The United States took in these individuals and their dependents as well.

These make up the post-war Vietnamese refugees. There is a "new" generation of Vietnamese refugees, almost entirely considered to be economic refugees or migrants. These people are fewer in number than the others and in Vietnamese communities are considered to be a separate category.

There was never any widespread fear that the Vietnamese refugees were communist infiltrators, though interestingly enough, a significant amount of the Vietnamese diaspora organized what could be considered terrorist or insurgent groups aimed at returning to Vietnamese to overtheow the communist regime.

Sources:

Chermayeff, Ivan. "The Vietnamese Migration." World Policy Journal 15, no. 1 (1998): 68-76.

Van Der KROEF, JUSTUS M. "The Vietnamese Refugee Problem." World Affairs 142, no. 1 (1979): 3-16.

Montero, Darrell. "Vietnamese Refugees in America: Toward a Theory of Spontaneous International Migration." The International Migration Review 13, no. 4 (1979): 624-48.

10,000 Still in 'Reeducation' Camps

Hoang, Tuan. "From Reeducation Camps to Little Saigons: Historicizing Vietnamese Diasporic Anticommunism." Journal of Vietnamese Studies 11, no. 2 (2016): 43-95.

David DeVoss. "A Long Way From Home: Some Vietnamese Immigrants Have Quietly Assimilated; for Others Who Yearn to Return Home, the War Goes On." Los Angeles Times, January 5, 1986.