Sister Joan Matthews' classroom at All Saints High School is filled with portraits of the Mother and Child, a crucifix, a blackboard dotted with dates of church councils -- and leaning over their Catholic liturgy texts, row upon row of Baptist, Methodist and Apostolic students.

To be sure, there are Catholics, too, in Matthews' class at the Northeast Washington school, but not very many. All Saints is 57 percent non-Catholic, one of 19 Catholic schools in the District whose student population is more than half non-Catholic.

In the past decade, non-Catholic enrollment in Catholic schools around the country has increased from 2 percent to somewhere between 12 and 15 percent, according to the National Catholic Education Association. But in some inner cities, and especially in Washington, that trend has been magnified several times over. The result, in the District at least, is a school system for black families -- mainly middle class, but also lower income -- who have spurned public schools. And because about two-thirds of blacks in Catholic schools are not Catholic, the schools' basic composition has shifted, causing some concern about who foots the bill.

"I really didn't choose a Catholic school," said Samantha Smith, a Baptist junior at All Saints, an all-girl, 99 percent black school in Brookland. "I went to a public school and there was a lot of fighting and negative things, so my family decided I should come here."

While the Archdiocese of Washington's schools in five Maryland counties remains overwhelmingly Catholic, enrollment in the District tells a different and rapidly changing story. An internal archdiocese study last year showed that one-third of students in Catholic high schools in the District follow other faiths. In the elementary schools, the non-Catholic population rises to 47 percent, with three schools having more than 70 percent non-Catholic students.

While some of those students go to Catholic school for religious content, many parents select parochial schools because of their reputation for discipline and academic rigor. "The school being Catholic didn't really matter," said Maria Lawson, a 10th grader who transferred from Jefferson Junior High to All Saints. "This is a better school. The only thing that's Catholic is the symbols, and as a Baptist, I just don't do them."

That trend has Catholic educators and parishioners asking whether Catholics who contribute to their church should pay to educate non-Catholics. Should Catholic schools limit non-Catholic admissions? Do non-Catholic majorities alter the character of Catholic schools?

"If you put an excess of any ingredient into a cake, it at some point ceases to be a cake," said Sister Maria Cincotta, who teaches English and world history at All Saints. "What is that excess? Ninety percent sounds like too much. But 75? I don't know. I can't define Catholic identity in numbers."

So far, no one has. While some Catholic schools require non-Catholic students to pay slightly higher tuition, usually about $250 more, no school has limited non-Catholic enrollment or even discussed it. But the Archdiocese of Washington asked Claire Helm, its assistant superintendent for elementary schools, to study the changes.

As white Catholics left Washington and other inner cities in the 1960s and '70s, some Catholic schools closed. Those that remained became predominantly -- and sometimes exclusively -- black schools attracting both Catholics and Protestants. Today, many inner-city schools get healthy subsidies from the archdiocese and 52 cents of every dollar contributed to the annual Archbishop's Appeal goes to education.

Helms concluded that "Catholic school is not Catholic because of numbers. Our schools are for Catholics. Schools are the best way the church can reach and teach its young. We welcome non-Catholics on the premise that parents accept that the schools are here to serve Catholic families first."

"We serve so many non-Catholics because we're Catholic," said Daniel Curtin, the archdiocese's secretary for education. "We offer a value system. We offer an alternative for people who found something lacking in other systems, public or private. If non-Catholics buy into that, they get the whole package."

That means non-Catholics and Catholics alike attend required religion classes every year. It can mean starting school with a spoken prayer and calling some teachers "Sister" or "Father." It means being taught Church positions against abortions, birth control and premarital sex. And it means attending Catholic liturgies on feast days.

"I only had one instance where two children said it would be against their practice to attend a Catholic liturgy and I didn't force them," said Sister Bernadette Glodek, head of high schools for the archdiocese and a former administrator at Notre Dame Academy. In most schools these days, attendance at mass is voluntary and sparse. Glodek said she called a voluntary mass at Notre Dame and got 50 out of 325 students.

But despite the lack of excitement about religious services, something educators attribute to inevitable adolescent antipathy toward rules and ritual, most non-Catholic students seem comfortable in a parochial setting.

Absorbing two religious traditions at once can be confusing. Tonya Colloway, a Methodist senior, said, "We were raised under different rules and we have to try to separate them." Senior Jacquie Herron, a Presbyterian, said her teachers "are kind of annoying. They're shoving it down your throats that you have to think like the church does." But such views are in the minority.

More typical are students such as Paula Holmes, a Baptist who said her Catholic education has "helped me find out who God really is. I go to Baptist church on Sunday and I'm going to raise my kids Baptist, but we're worshiping the same God. It's just written differently."Catholic Beliefs Taught

All Saints' religion curriculum begins with a course in Scripture, focuses for a year on church history and Catholic sacraments and then devotes two years to morality, social justice, marriage, family and issues such as abortion and capital punishment.

The impact varies. Tenth grader Linda Cole, a Baptist, said she has found few differences between the two religions. "They're alike to me. Baptists, we stay in church longer and the ladies have to wear skirts and dresses."

"They teach you basic Catholic beliefs," said Latanya Smith, a senior who is Baptist, "but they also teach you basic Christian beliefs."

Exactly the point, says Sister Sheila Powers, who teaches All Saints' senior religion class. "All these kids come from committed Christian families and we teach the Christian character, basic values. There could be a secular humanist in this class and they wouldn't disagree with most of the material."

In class, Powers is as likely to present as role models Sojourner Truth, Martin Luther King or figures from the Harlem Renaissance as she is to use examples from the Catholic past. In his junior morality class, Keith Williams taught about the equality of man by quoting from Malcolm X, Elijah Muhammad and even Nation of Islam leader Louis Farrakhan.

Still, religion classes and texts do teach official church positions, and to a generally receptive audience. Only on the most controversial issues do some students chafe at church teachings.

"The Protestants tend to be much more rigid on some sexual and moral issues," Powers said. "The view of the human person as being basically good is a Catholic view. The view of humans as fallen is basically Protestant."

In the classroom, Protestant students are often more outspoken, more likely to challenge official positions than Catholic classmates, teachers said. They blame Catholic traditions of rote education, mandated prayers and dry, even somber ritual, in contrast to Protestant -- and particularly black Protestant -- traditions of encouraging individual expression and joy in religion.

"We Catholics do tend to be square in church," Matthews said. "Black Protestants are freer emotionally in their faith. That's why many black Catholics feel there's a gap in our religion." Matthews tells of a student who converted to Catholicism but still attends her mother's Protestant church to shout and sing. "All that sharing in their younger years shows up in the classroom where they are very outspoken."

Catholic students sometimes talk about their Protestant classmates, said junior Audra Latney. "A lot of people say the non-Catholics are bringing the school down, but it's really not true. Most of the teachers don't even know who is Catholic."

But with Protestants dominating some schools and classroom discussions, Catholic educators have begun to ask basic, troubling questions.

The Catholic school system, created at the Council of Baltimore in 1884, was never intended to convert outsiders. It was to be an alternative for immigrants of the period, a generation of "children who perceived hostility to Catholic values in public schools," said Michael Guerra, executive director of secondary schools at the National Catholic Education Association.

The focus of Catholic education has always been to provide top-quality education infused with traditional Catholic values. Then came the opening of America's suburbs and white flight from the cities. Some urban Catholic schools closed or moved to the suburbs. Schools that remained became increasingly black and non-Catholic.

"The mission of the schools shifted to accommodate new populations," Guerra said. "The schools remain committed to a religious purpose, but in a way that doesn't impose on the beliefs of non-Catholic students." Exactly how that theory shows up in the classroom varies from school to school.

While morning prayer, community service programs and mandatory religion classes remain staples of Catholic schools, other parochial traditions have vanished from some places. Few faculty members at All Saints wear habits anymore and the number of lay teachers increases steadily. Religion teachers say their discussions of moral and ethical issues are often based in Judeo-Christian beliefs rather than specifically Catholic teachings.

Such changes have led to new definitions of Catholic education. "We exist to impart Catholicism," Cincotta said. "Clearly it isn't our intention just to be a better school. I don't for one minute feel that because I'm not teaching religion that I'm not imparting Catholic teachings. I am doing the Lord's work, even if I am teaching 60 percent non-Catholics." A 'Value-Laden Education'

Guerra wouldn't disagree, but phrases it differently: "Catholic schools provide an overtly value-laden education."

The difference between imparting Catholicism and teaching values is more than semantic, teachers say. A school without Catholic students would somehow not be a Catholic school. But when does that change occur? Is there a tipping point?

Powers rejects limits on non-Catholic admissions. "That's discrimination," she said. "It's a terrible thing to say in an ecumenical age and it ends up being a racist statement because the urban areas are where the non-Catholic students are. Catholic schools are a luxury in the suburbs. The place where they're really needed is in the cities."

"Well, the Catholic population might have something to say about that," Matthews said. "In justice to the Catholic people who donate so much to the schools, limits may become an issue."

For now, the Catholic system needs -- and wants -- non-Catholics. The church has an obligation to serve urban children, adminstrators say. And with overall enrollment on the decline -- systemwide enrollment dropped 2 percent last year and the archdiocese closed one elementary school -- non-Catholics help keep schools thriving, both in bodies and dollars. Tuition at Catholic high schools ranges from about $1,800 to $5,000 a year.

"I would be very reluctant to establish a litmus test for defining a Catholic school," Guerra said. "It is certainly something we agonize over, especially in a time of limited resources. Is this a legitimate mission of the church? So far, the answer is yes."