The budget thunder out of Washington these days finds many people running for cover, carrying their favorite programs, like valued possessions, to higher ground in the hope that the coming flood won't wash them away. Most are running scared and confused with no coherent resistance, no principled opposition. The New Deal's out, austerity's in, and woe to those who dally while the budget-cutters sharpen the ax.

For once, New York City may be in a position to offer some advice on budgets; we certainly know a thing or two about how to cut them. And we have learned a lesson: When it comes to cutting the budget, you need the skill of a neurosurgeon, not the sweep of the butcher. Unless cuts are carefully crafted, they may result in greater costs down the road. Simply stated, we have found that an ounce of prevention is worth a pound of cure.

So far, the Reagan administration has not heeded this valuable lesson. One of the most flagrant examples of misguided budget-slashing came recently from Human Services Secretary Richard Schweiker, who called for the elimination of federal funding of sex education and contraception for teen-agers, thus ignoring social reality. Teen-age pregnancy is epidemic through-out America; last year in New York City alone, 14,259 teen-agers gave birth. What happens to these mothers? If they survive childbirth, when their chances of dying are 60 percent greater than for women in their 20s, almost three out of every four (72 percent) will end up on welfare. In New York City alone, the yearly welfare costs for these new teen-age mothers is $39 million.

The tragedy is even more dramiatic in human terms. Many of these children are inadequately cared for or are abused and end up in foster care, where they languish for years. When child abuse occurs, not only the direct perpetrator will be responsible. So will all of those who remove the thing preventive safety net that now exists for at least some of these teen-agers. Does it make any sense to eliminate the marginal expense of current sex education and contraception programs? Does anyone really believe that prevention isn't the wisest course here?

One wants to give the Reagan administration the benefit of the doubt. But one fears there may be a method in its madness -- perhaps this budget-cutting isn't so blind after all. Remember the campaign, and all the Moral Majority-inspired talk about the "decline of the family"? Sex education and contraception, it seems, threaten the family's hegemony and must be stamped out.

If necessary, we can remind the Reagan administration that the challenge for government policymakers today is to mount a concerted response to the tremendous behavioral changes that are redefining the American family. Today, 58 percent of all husband-wife families have two or more wage earners, 32 percent of married couples have no children living at home and one out of seven families is headed by a single parent. It is estimated that more than one-half of the country's 21 million teen-agers over 15, and approximately one-fifth of those under 15, are sexually active.

Withholding information about birth control will not preserve the family. President Reagan would better serve us all by recognizing the changes now taking place in the nature of the family unit and confronting the challenges of the future, rather than looking back to a past that no longer exists.