NOW THE FEDERAL Department of Education has begun nudging the states to delay compliance with the Supreme Court's decisions. The secretary, William J. Bennett, is particularly affronted by the Felton decision last month holding that New York City cannot send public school teachers into parochial schools to provide supplemental instruction to children from poor families.

He wrote the state school superintendents a letter last week reminding them that he disagrees with the court and sympathizes with the "confusion" that the decision is causing. But of course, he went on, the states must comply with it. He then noted the pending litigation over requests for delays and said: "This department will support local and state agencies in litigation, who have good grounds for requesting necessary delays in implementing the Supreme Court's decision." But of course, he repeated, school boards must make every effort to comply as soon as possible. Taken all together, the letter amounts to a pretty broad suggestion that, if local school authorities want to drag their feet, they have a friend in Washington.

The school aid questions are exceedingly difficult. Congress decided two decades ago that handicapped children, and children living in poverty, were entitled to special educational benefits whether their schools were public or private. Congress knows that churches run fine schools in this country's bleakest slums, and the Catholics in particular have put extraordinary resources into parochial schools in desperately poor neighborhoods where most of the children are black and Protestant. Nobody wants to cut these children off from federal aid. But that leaves the courts with the onerous job of deciding how it can be delivered without violating the Constitution -- how to help the church schools' children without helping the church schools. Some of the decisions here are very close calls.

In the Felton case the court was divided, typically, by 5 votes to 4. Mr. Bennett's strategy of delay carries an unpleasant hint of anticipation of personnel changes in a court in which most of the present justices are in their seventies. Perhaps a newcomer would tip the court the other way.

When the Education Department was established under the previous administration, conservatives objected that it would rapidly become a vehicle for entangling the country's schools in the political interests and intentions of successive administrations. Those conservatives turn out, unfortunately, to be quite right. Have you noticed that the Reagan administration hasn't had much to say lately about the desirability of abolishing the department?