American families are profoundly concerned with their health, but few are doing much about it. This is a prime conclusion of a new survey released yesterday for the American Family Report of General Mills.

The study, by Yankelovich, Skelly and White, involved 1,254 families.

Inflation took the blame for cutbacks in health-care practices among almost half the families surveyed, 48 percent. It was worse among low-in-come families (56 percent), minorities (60 percent) and most of all, single parents (72 percent).

As Dr. Eleanor G. Shore of Harvard, a consultant in the survey, put it: "The public lacks the scientific knowledge to understand fully the relationshiops between their behavior-smoking, drinking, overeating, drug use-and cancer, heart disease, strokes and mental illness."

Though more people are exercising than were a year ago, though the national fiath in doctors and dentists is holding firm (in contrast to many other institutions), though we are becoming more wary of pill-taking, there is little sign that our deeper biases on health have changed so far.

For example, three out of four continue to see mental illness in terms of social stigma. Alcoholism, depression, child abuse, nicotine addiction, even overweight-all are considered personal emotional weaknesses rather than health problems.

Underweight, however, is viewed as strictly a health matter. Speaking of diet, the most serious health threats seem to be, in order, crash diets, overweight, diet pills, pesticides, cholesterol, chemical fertilizers, fasting, fats, food additives and sugar - a list that reflects nutritional issues currently in fashion with the media.

The survey detected curious ambivalences in American attitudes about health: We fear cancer more than anything else, yet only 1 in 4 believes a checkup is the only way to find out if we are healthy. The rest feel themselves healthy as long as they notice no particular symptoms. And 54 percent, despite their concern about serious disease, believe "it couldn't happen to us."

Though accidents are the second most feared health hazard, 17 percent of families admit they don't keep medicines out of children's reach. And though alerted to the problems of overmedication (largely by the news stories about Betty Ford, the surveyors suggested), families appear to fell better about technology in general than they did last year, and some 76 percent believe that a cancer cure is "just around the corner."

More than 80 percent of the subjects spoke of "stress" as making life harder to cope with than ever. One source of stress is confusion over frequent government warnings about this or that product or food, notably saccharine.

Yet most family members said they would go to a psychiatrist or psychologist only as a last resort.

Another ambivalence: For all their fear of accidents, 63 percent of American families often don't fasten their seat belts.

At yesterday's conference, press queries indicated difficulty with some of the survey's language, which often seemed rather general. For instance, the liquor-marijuana issue, a complex mix of socioeconomic factors, is handled this way:

"While studies in the past have indicated that parents were more afraid of their teen-age children's using marijuana than they were of their drinking liquor, this no longer is true. Only 1 out of 3 parents of teen-agers (36 percent) would prefer to see his or her teen-age children drink than smoke marijuana, while 2 out of 3 (64 percent) would not."

A sample of the survey's yes-no approach:

"Now that women with children have taken jobs outside the home, the health of their children suffers"-Yes, 39 percent. "Working women take as good care of their children's health as mothers who stay home"-Yes, 61 percent.

Most press questions concerned government's role in health care. Four in 10 Americans feel the "government" should see that all Americans have good health care whether they can afford it or not. Sixty percent say it's up to the individual family.

On the other hand, 58 percent "favor a national health bill because it will help all Americans" while 42 percent oppose such a bill "because it will just be another giveaway program that will cost the taxpayer money."

Commenting, surveyor Deborah Barron said that most of those tested "didn't know what we meant about national health," believing it to be something like the British system or publicists Whitaker and Baxter's slogan, "socialized medicine."

Summarizing the findings, here are some highlights on the positive side:

Most Americans are more concerned about preventive health care than in the past.

The "new values" detected by Yankelovich in the past 20 years-interest in self-realization perhaps even more than material gain-mean that more people are trying to take as good care of themselves as they can.

More Americans are "concerned" than "complacent" about their health (60 to 40 percent), 1 out of 3 is exercising several times a week, and 1 in 4 is eating better and counting calories more than before.

Along with a greater awareness of dangers to health, from salt to cigarettes, comes a backlash to the medication fad that has made miracle drugs, tranquilizers and pills generally a part of the American scene.

On the negative side:

Subjects blamed the stresses of life, their own ignorance and lack of self-discipline, plus the high cost of medical care, for poor health care.

Inflation is cutting into food quality, meat-at-meals, dental work, annual checkups, getting new glasses and various preventive techniques.

As Dr. Donnell D. Etzwiler and advisory panelist, said, "People take their health for granted; they assume that because they've always been healthy, this will continue without any effort on their part."

Permissive parents were scored for lack of discipline in children's health habits. At the same time, 8 in 10 parents of teen-agers felt it was their job as parents, not the schools, to teach the children about birth control.

We continue to view mental illness as a personal weakness, though we give lip service to the concept of it as a health problem. Subjects said they would be reluctant to seek professional help with: insomnia (76 percent), smoking too much (72 percent), children's problems, marital problems, depression, anxiety, fatigue and drinking problems.

"Fewer than 3 out of 10 American family members qualified as well-in-formed about health," by their own reckoning.

The survey is the third in a series of reports on the American family funded by General Mills. "Raising Children in a Changing Society" was issued in 1977, and "The American Family and Money" in 1975. The sample included 2,181 individuals from the 1,254 families, breaking down as 664 spouses and 263 teen-agers.