What do James S. Coleman, the liberal sociologist, and Ronald Reagan, the conservative president, have in common?

Both seem hell-bent on unwittingly destroying public schools.

Reagan has supported tax breaks to parents who send their children to private or parochial schools, and last week Coleman released the results of a huge study claiming that private high schools are better than public ones, which has added support to the Reagan view.

But all of this -- diminishing respect for public education and the possibility of public financial aid to help parents keep their kids out of public schools -- will do little to improve the dismal state of most big city schools. The Reagan/Coleman view may even make matters worse.

You may remember James S. Coleman. In the mid-1960s, an influential Coleman study concluded that black children learn better in integrated classes. That study was used to support school desegregation -- and busing to achieve it.

More than a decade later -- after years of street confrontations between those for and those against forced busing -- Coleman announced that he'd come to believe that black children don't necessarily learn better in integrated classrooms, which must have come as quite a shock to the parents and school officials in battle-weary Boston.

By 1978, Coleman had concluded that a tuition tax credit for parents sending their kids to private or parochial schools would help low-income black parents afford the cost of getting their kids out of public schools. Today, that view fits neatly with Coleman's recent conclusion that private high schools are better than public schools.

But James P. Comer, a noted Yale University child psychiatrist, and other advocates of public education disagree vehemently with the public policy implications of Coleman's view. Perhaps the strongest response comes from The National Education Association: "Irresponsible public policy research," association spokesperson Sharon Robinson called Coleman's study. The debate over Coleman's report will go on and on.

But what bothers me most about Coleman is his gall. He helped bring us the traumas of busing and then had the luxury of changing his mind. Now he is back again, recommending governmental policies that will encourage even more parents to abandon public schools, leaving behind even a greater wasteland than already exists in most city schools.

This is not a view government -- even Reagan's government -- can afford to adopt. And it does not have to be.

In his recent book, "School Power," Comer argues that public schools can succeed. In New Haven, Conn., the Yale Child Study Center he heads "intervened" in two schools in which 50 to 80 percent of sixth grade students were reading below grade level. More than 50 percent of these children lived on welfare. They often missed school and when they did attend, often misbehaved. Morale among staffs and parents was low. In short, these were typical inner-city schools.

"Intervening" in these circumstances should be the colossal task of government today -- not finding ways to run away. School administrators and teachers are unrealistically expected to deal with all the problems of society -- drugs, racism, poverty -- without needed training or help from social and mental health organizations, Comer says.

That is what he set out to change in New Haven. He brought school officials, teachers, parents and mental health specialists together around these sixth graders -- not only to deal with their ability to read and write, but the very conditions of their lives. It worked; the kids did a turnaround.

Their test scores in reading and mathematics increased significantly; parent participation soared. Where once 15 parents might turn out for a school function, now 400 come.

Comer wants to duplicate the success in other schools -- but his work is threatened because it depends in large part on funds set to be cut by the Reagan administration. That piece of information alone tells much about the impact governmental cutbacks can have on obscure but important programs, how deciding to put public money into helping private schools instead of public ones can indeed make a difference.

The solution growing from the views of James Coleman and Ronald Reagan -- send the kids who can afford it to private schools -- is shortsighted, even disastrous. It may be the answer for individual parents rightfully worried about the few years their child will spend in high school. But it is not a solution that should be stamped with the imprimatur of government.

The problems of public schools graduating illiterates, serving as baby sitters, guards, psychologists, doctors, parents and educators at once can be ignored now in favor of the few of us who can escape to private schools. But 20 years from now, the children we protected, will have children and grandchildren of their own to protect. All of them may not make it into private or parochial schools -- tax break or not.

And by then, who knows? Coleman may have changed his mind still another time. After all, he has that luxury.