Pope John Paul II'S week-long visit to America in October, which could end up costing $10 million, has set off heated separation-of-church-and-state squabbles over who should pay the bills.

Civil liberties and Protestant groups yesterday challenged proposals in Philadelphia and Boston to spend public money on facilities for outdoor papal masses planned in those two cities.

In financially hard-pressed New York, city and Roman Catholic officials were locked in negotiations over who should pay various costs.

Here in Washington and in Chicago and Des Moines-- the three other cities the pontiff is scheduled to visit from Oct. 1 to 7-- there appeared to be little dispute yet about how the costs will be split. The church in those cities plans to shoulder all religious service-related construction costs, with the cities picking up what they expect to be enormous costs in police overtime, trash pickup and large scale transportation arrangements.

With two Protestant ministers and the Massachusetts Civil Liberties Union objecting strenuously, the Boston City Council debated appropriating $150,000 to build two platforms for an altar and 300-member choir on the Boston Common where the pope will celebrate mass on Oct. 1, his first public service of the seven-day tour.

"The construction of those two platforms for the conduct of the mass seems to us to be direct aid to religious service," said Ernest Winsor, president of state civil liberties union.

"Is it appropriate to spend public tax dollars, public tax money, for a religious service on the Boston Common?" asked Kennth Claus, a United Church of Christ minister.

Church leaders in heavily Catholic Boston contended the pope's visit will amount to a "public celebration" comparable to the visit of Queen Elizabeth during the bicentennial in 1976. Catholic officials noted that the queen is both head of state and head of the Anglican Church in England.

"It's a toughie, it's a close call," said Lawrence DiCara, a member of the Boston City Council.

In Philadelphia, Mayor Frank Rizzo triggered angry reaction from local civil liberties attorneys yesterday when he announced on a television talk show that the city "will pay the cost" of building a platform from which the pope will celebrate mass outside the city's Catholic cathedral.

This "is a clear violation of all citizens' rights," said Hilda Silverman, director of the Philadelphia office of the American Civil Liberties Union.

"We'll write a very strong letter [of objection]," she said. "If we have to, we'll sue."

Undaunted, Rizzo said, "The church offered to pay for it but I think it's our [the city's] responsibility." He said he did not know what the cost may be, but "whatever it would be, it's well worth it."

As Protestants, Catholics and assorted civil libertarians debate what constitutes transgression of the separation-of-church-and-state doctrine of the U.S. Constitution, Catholic officials are taking great pains to emphasize that the pontiff will be here as a religious rather than a political leader. The United States does not recognize the Vatican as a political entity.

"Nobody has any problems putting up [public] money for clean-up, police overtime, police protection (and) traffic control," said Ed Doerr, spokesman for Americans United for Separation of Church and State. It is the use of tax money for the construction of facilities expressly intended for religious rites that is wrong, he said.

"The only thing we're taking issue with is this damned platform" for the papal mass in Boston, said John Robert, head of the Boston ACLU office.

In New York, church and city officials have been discussing who should foot which bills, but the officials would give no details.

"It's being discussed . . . but it's premature for us to talk about costs," said spokeswomen Alice McGillion in the office of Mayor Edward Koch.

The pope is scheduled to appear at city-owned Yankee and Shea stadiums and Battery Park, as well as privately owned Madison Square Garden.

McGillion said that, as an example, there "may be some discussion-- I wouldn't call it negotiations-- about building a platform in Battery Park and the cost."

New York archdiocesan officials declined to comment, saying details of the New York visit will be announced later.

In constrast to the situation in Boston and Philadelphia, church officials plan to pay for the construction of altars and other facilities here in Washington and in Chicago.

The Archdiocese of Chicago announced it will spend $100,000, including $50,000 for a 15-foot high altar in Grant Park for the pope's scheduled outdoor mass there Oct. 5.

Similarly in Washington, church officials estimate they will spend $400,000 for an elaborate 10,000-square foot, three-tiered stage and altar and other facilities for the pope's mass on the Mall planned for Oct. 7.

In Des Moines, where the pontiff will make a quick four-hour visit on Oct. 4, church officials say they plan to spend up to $1.5 million, defraying some of the costs by selling religious memorabilia.

District of Columbia officials say it is too early to be specific, but city costs associated with the pope's two-day visit here should come to $1 million to $1.5 million, most of it in police overtime. U.S. Park Police estimate overtime for their smaller force will about to about $80,000.

Cost estimates from the church and the cities indicate the seven-day papal visit may total $10 million or more.