Even though the nation's Roman Catholic archbishops have approved their historic pastoral letter condemning nuclear arms, millions of American Catholics went to church this morning facing the same moral decisions they faced last week.

The bishops approved a strongly symbolic document that renounced a nuclear first strike under any circumstances, called use of nuclear weapons on civilian populations "morally unjustifiable" and conflicted sharply with some parts of U.S. strategic policy.

But, while the 150-page pastoral was hailed by the bishops and the growing nuclear protest movement as a pivotal moral statement, its immediate impact on workaday Catholics is less clear.

The bishops stressed that their moral judgments on specifics such as "no first use" are "to be given serious attention and consideration" but are not morally binding on Catholics. In a news conference at Trinity College here yesterday, Washington Archbishop James A. Hickey said the Vatican is "very anxious" that bishops keep that distinction.

But the distinction left American Catholics, including defense workers and military personnel who deal with nuclear weapons, in somewhat of a quandary: while they now have moral guidance from their bishops, they also have the right to disagree.

Even among bishops who support the letter, disagreement is wide, just as it is expected to be this morning in the nation's Catholic churches. Some of the disagreement emerged just days after adoption of the letter Tuesday in Chicago.

San Francisco Archbishop John R. Quinn, long an outspoken critic of the arms race, said the action means that Catholic military officers should refuse even a presidential order to detonate a nuclear weapon. He said such an order would be "morally wrong" and would exceed the president's authority.

But Cardinal John Krol of Philadelphia, one of the pastoral's strongest backers, said at Trinity yesterday that the bishops' position does not go that far. He described the letter as a "teaching document" with which the church can widen its debate and educational effort on nuclear weapons.

Some of the statement's key architects steered far from giving specific instructions to Catholics in the military and defense industries. The Rev. J. Bryan Hehir, the bishops' chief adviser on the nuclear issue, said here yesterday that moral decisions--even on such strongly worded parts of the statement as its denunciation of use of nuclear weapons against civilians--would be left to individual Catholics.

Asked if the Catholic pilot of a nuclear bomber, knowing his target is a Soviet city, should reject his orders on moral grounds, Hehir replied: "The bishops have spoken on that issue, but I cannot make the decision for that man."

Hehir said he is reluctant to "boil down a 150-page statement to a single sentence."

After their two-day Chicago conference, the bishops were generally elated that they had acted almost unanimously in the 238-to-9 vote. But most also expressed certainty that the pastoral is the beginning, not the end, of the church's moral wrestling over nuclear arms.

The consensus was that the letter provides a teaching forum, blessed by church authority, but leaves great latitude on practical applications by laymen and individual priests.

Archbishop Peter R. Gerety of Newark, N.J., said the next great challenge is "teaching the document" and warned that "there will be heated discussion."

In its directions to individual Catholics, the pastoral is muted and carefully worded. The bishops told parents that their role was "unsurpassed" in rearing children who "solve conflicts through nonviolent methods," enabling them to "grow up as peace makers."

But for defense workers and military personnel, the letter leaves decisions open to individual interpretation, calling on Catholics to use the document's moral principles to "form their consciences."

The letter tells Catholic defense workers that the bishops do not "presume or pretend that clear answers exist to many of the personal, professional and financial choices facing you . . . ." The directions to defense workers are made even more open to individual choice by the bishops' "conditional" acceptance of the policy of nuclear deterrence.

The bishops tell defense workers that "those who in conscience decide that they should no longer be associated with defense activities should find support in the Catholic community." But the letter also instructs those who remain that they can "find in the church guidance and support for the ongoing evaluation of their work."

Almost two years ago, Archbishop Leroy P. Matthiesen of Amarillo, Tex., told Catholic workers at the nuclear-arms assembly plant there that their work was immoral and they should quit their jobs. His outspokenness, however, was greeted mostly with derision in the conservative Texas Panhandle city and few Catholic workers left their bomb-assembly jobs.

The pastoral is couched in even more cautious terms in its directions to military personnel, saying it is "surely not our intention . . . to create problems for Catholics in the armed forces."

But every profession "has its specific moral questions," the bishops write. To the military, they say, those questions include use of weapons or tactics that "inflict harm on innocent civilians."

The letter leaves unclear where the military should draw the line, but states that refusing unlawful or immoral orders "is not an act of cowardice or treason but one of patriotism."