Does Sweden's social net save or entangle family life?

How can mothers, fathers, and children, all going their separate ways during the weekday, be helped to find more in common when they do get together? ''The working week should be cut here to 30 hours - six hours a day - to give working mothers, especially, more time to be with their children,'' is one prompt answer from prominent sociologist Carl Gustaf Boethius in this Nordic country.

Mr. Boethius, tall and precise, is vice-president of a Swedish association that promotes family and sex education in schools, and he is editing a book entitled ''Why has it Become so Difficult to Stay Together?''

''Also, the state should greatly increase the allowances paid to parents for each child,'' Mr. Boethius said in an interview.

Mr. Boethius is one of many in Europe today asking how family life can be strengthened, rising divorce rates lowered, and European birthrates raised. They are speaking out at a time when prolonged recession has made governments worry that extensive European welfare networks must now be cut back, despite the political controversies involved.

With spending cuts possible, governments from London to Vienna wonder whether they might just turn out to strengthen family life rather than impede it. Opponents say that this is merely rationalizing. Proponents claim deeper issues are involved, including individual freedom from state control.

Sweden has been famed for the extent and depth of its welfare state. Now even the new Social Democratic government is looking for fresh ideas. In fact, it is considering a shortening of the workweek - and has just proposed increases in child allowance payments.

''So many young women are working these days, to express themselves and because they need the money,'' Mr. Boethius said. ''Men work. Children are in school. All develop in different ways. When they come together, they often argue and find little in common. . . .

''As well as seeing their parents more often, children need to be taught to listen more. Both parents and children need to value the family more and selfish self-expression less.''

Here in northern Europe, just as in Britain and the United States, the question of how to strengthen the family is causing more and more stir.

The divorce rate has been soaring - from 1 divorce for every 6 marriages in 1966 to more than 1 for every 2 today. More young mothers work part or full time.

Fewer Swedes go to church compared with a decade ago: Officially 94 percent belong to the Lutheran Church but surveys show about 11 percent are believers.

The family as a unit has by no means disappeared, but it has changed its shape and form. While the number of marriages themselves has fallen (from 61,000 a year in 1966 to 38,000 by 1981) more 20- to 24-year-olds are living together than ever before, both here and in Denmark. A number of these couples marry after having one or two children.

But the birthrate has dropped considerably. According to Erland Hofsten, chairman of the European Center for Population Studies, 123,000 children were born in Sweden in 1966 but only 94,000 in 1981.

Now politicians as well as teachers and parents are beginning to ask how young parents in particular can sort through today's shifting values to reach a firmer, more soundly based relationship with each other and their children. If they can, not only the families but all of society would benefit.

Prime Minister Olof Palme is so concerned that he has set up a special commission under his own chairmanship to generate new policy ideas to help children and youth in trouble.

''We cut across ministry lines,'' commission member Soren Kindlund told me in the Cabinet office on the Stockholm waterfront. ''The new government only came in last October so we are still just starting out, but we are looking at dropouts, crime, drug-taking.

''You can't stop parents divorcing with a law. We are looking at what instruments our society might have to help.''

Many commentators think young women will not stop going out to work because the state pays them extra child benefits. That has been shown in France among other countries.

Nonetheless, the Palme government is boosting child allowance payments - to 3 ,300 Swedish kroner (about $450) a year for the first child, the same for the second, $665 for the third, and $885 for every additional child.

Sweden has about 1 million families with 1.7 million children under age 16. About 74 percent of all women between the ages of 20 and 64 hold some kind of outside job.

Parents between them are already allowed 12 months leave of absence for a new baby, with nine of those months on state aid equal to 90 percent of their wages. Legally, both parents can shorten their working hours by one-quarter until a child is eight years of age.

In fact, young parents tend not to take full advantage of the rules because employers warn them about loss of promotion, it is reported. Twelve percent of young fathers take paternity leave, he says, but many stay home only for a week or two.

The Palme government is spending more on transportation facilities for the elderly and providing social help in their homes. It also plans to reduce taxes on allowances designed to help parents care for disabled children.

Nonetheless, much more new thinking is required, and Mr. Kindlund's commission is in the middle of it.

''In particular,'' he said, ''we are looking into how children can take more responsibility for themselves - running their own school cafeterias on a cooperative basis, for instance, and supporting and counseling their own classmates who have turned to drugs.''

For a Social Democrat, he sounded surprisingly firm in echoing a line taken by Prime Minister Margaret Thatcher in Britain: ''Of course the state needs specialists in health, and education, but we (do not want) to build up state welfare anymore. We want people to do more for themselves.''

Mrs. Thatcher has set up a Family Policy Group at 10 Downing St. to find ways of taking the state out of people's lives wherever possible. There are some signs of hope in Sweden. Sociologists, parents, and young people tell Mr. Boethius that more young fathers are now sharing housework and baby care, instead of spurning such tasks as their fathers and grandfathers did.

Soren Kindlund agrees. So did another social policy expert consulted by the the Monitor. This writer was struck by the number of young suburban fathers around Stockholm pushing baby carriages and carrying children on their backs.

Mr. Boethius also sees a shift in the feminist movement in Scandinavia and the US. Danish author Jette Drewsen, he says, is arguing that the women's liberation movement must now ask how to live after liberation and whether women take enough responsibility at home.

Betty Friedan, American author of ''The Feminine Mystique,'' has just been in Sweden stirring up controversy but winning some support with her argument that women must stop hating men and start cooperating with them at home.

In Sweden, Barbro Leneer-Axelson has written that not all divorces are justified these days. Many of them, she believes, are caused by a wife or husband self-centeredly following a new infatuation. Instead couples should be trying seriously to work out solutions for the sake of their children.

Mr. Boethius sees more young people trying to solve marital differences because they have never forgotten the experiences of their own parents' divorce. Meanwhile he also sees some renewal of religious interest in Sweden. Lutheran Church attendance is up. But the renewal is too new to have affected family behavior, he says.