After 25 years of governmental indifference and disagreement, the people who were once regularly exposed to radioactive fallout from U.S. atomic bomb tests have finally made major progress in getting officials to hear their claim that the fallout caused leukemia and cancer.

Their successes come at a time of growing evidence supporting their assertion that, as one lawyer puts it, "they were citizen-soldier casualties of the Cold War."

The University of Utah had disclosed that an as-yet-unpublished study by its researchers showed at least "cause for concern" over the nuclear testing program and the incidence of leukemia and cancer in southern Utah.

In the 1950s, complaining residents of the fallout zone -- tens of thousands live scattered over the rural areas of three states declared "virtually uninhabited" by the old Atomic Energy Commission -- were dismissed out of hand.

But last week President Carter took three steps toward taking up their cause. It was a stark reversal from the congressional response to the 1977 petition from survivors who wanted protection from atomic testing. That was greeted with references to "communist-inspired scare stories." Several of the signers of that petition have since died of cancer.

In addition, Utah Gov. Scott M. Matheson now sees the possible adverse health effects of a decade of nuclear testing as "the biggest public health issue in the state." He is expected to ask the legislature next month for money to begin dealing with it.

The entire Utah congressional delegation has joined to pressure the White House and the Department of Health, Education and Welfare to ascertain what illnesses, if any, were caused by the tests and to help any victims or their surviving relatives.

And the residents here recently formed a "committee or survivors" to locate scores of leukemia and other cancer victims to document the connection they see between widespread leukemia and other cancers and exposure to the radioactivity.

They are finding victims in numbers far beyond their own fearful expectations. In addition, many have either filed, or plan to file, wrongful death claims with the government, seeking tens of millions of dollars in damages as compensation for what lawyers say may be several hundred deaths and illnesses.

Besides compiling the names of those who suffered and died of cancer in the scattered small towns and on the big ranches of the fallout zone, the committee of survivors has found former residents like Pamela Olsen, a 24-year-old leukemia patient, living with their diseases in other parts of the country.

Their wrenching illnesses have produced financial hardship, emotional strain and personal loss.

In California last month, relatives of an elderly woman dying of leukemia waited for a nurse to remove an intravenous needle from the woman's hand so she could sign a formal claim for injuries against the government.

"We're really just scratching the surface," says J. MacArthur Wright, an attorney here, who, with former interior secretary Stuart Udall and Tucson lawyer Dale Haralson, is representing the committee of survivors.

His office has become a virtual command post where the telephones daily bring additional reports of cancer. The committee is trying to gather enough such cases to prove that those who lived here during that testing period have a higher rate of leukemia and cancer.

The canvassing, Wright says, has already found for adjoining ranches in Utah where the husband and wife on each ranch either died from or suffered cancer. Matheson became involved in the issue after he was given a list of victims. It included some relatives.

At least 84 atomic weapons tests were conducted from 1951 to 1962 at the Nevada testing site. There were no tests above the surface from 1959 through 1961, and since the limited nuclear test ban there have been five nonweapons atomic tests above the surface as well as at least 18 accidental ventings from underground tests.

The radioactivity spread across the rural areas -- officials would not detonate the bombs if the wind blew toward Las Vegas -- onto the hay and feed for the cattle and dairy cows, onto the gardens and produce farms, the mines, the quarries.

The federal government has rigidly maintained that the tests were carried out safely and without hazard to those living downwind.

Officials have cited one study of thyroid abnormalties (which can be caused by radiation) among schoolchildren that showed no unusual incidence. But The Washington Post reported last July, in a detailed account of large numbers of leukemia deaths here, that the Food and Drug Administration now thinks that thyroid study stopped too soon, and that it would be reopened.

That was one of three actions cited by Carter last week. The president also directed HEW to review a series of studies into unexplained clusters of leukemia cases in Utah and Arizona, studies disclosed by The Washington Post last July.

The president also directed federal officials to confer with state health investigators to determine whether there should be an extensive investigation of persons affected by U.S. fallout, such as those who live in Japan and in U.S. A-bomb test areas of the Pacific Ocean.

One of the persons in Utah who thinks that she sould be a part of such an investigation is Pamela Winemiller Olsen.She and Mark Olsen who as St. George schoolchildren had been through the thyroid-screening study, married and moved off to Salt Lake. There followed three boys, Adam, now 7, Sean, 5, and Ryan, 2.

Olsen was able to make a downpayment on a gas station in 1976, the Texaco station in Bountiful. But before a year passed, while boby Ryan was but a few months old, Pamela Olsen, hurting, sick and hospitalized, was told bluntly and without sugar-coating that she had acute leukemia.

"It was just so devastating," she recalled to a visitor at her home the other day. "My doctor told me if I made it through chemotherapy I could live a year or two years."