WASHINGTON (AP) _ The National Endowment for the Arts, shaken by a conservative furor over subsidizing ''obscene art,'' is getting a new chairman this week who promises to strike a balance between freewheeling artistic freedom and respect for the public's trust.

''We are not the nation's official pornographer, and it's important that the country know that,'' said John E. Frohnmayer, a 47-year-old lawyer from Portland, Ore., who takes command of the beleaguered arts endowment Tuesday.

Nonetheless, some members of the cultural community are expressing fear that the bitter controversy over the endowment's role in financing controversial art might undermine future support for bold, innovative - and unpopular - artistic ventures.

The worst political crisis in the NEA's 24-year history began earlier this year when conservative members of Congress were outraged to discover that $45,000 in endowment funds had been used to support two exhibitions they found offensive.

One featured works by the late photographer Robert Mapplethorpe that included homosexual and sadomasochistic themes and pictures of nude children. The other show, by artist Andres Serrano, featured a photograph of a crucifix submerged in a container of urine.

In a surprise move, Jesse Helms, R-N.C., won Senate approval of his sweeping proposal to prohibit spending federal funds on ''obscene and indecent'' art or any work that ''denigrates, debases or reviles'' anybody on the basis of race, creed, sex, handicap, age or national origin.

His amendment to the arts endowment's $171 million appropriations bill caused a furor in the arts community, and House-Senate negotiators finally produced a compromise last week that contains a watered-down version of the Helms proposal.

The legislation, awaiting action by President Bush, would bar government financing of works that ''may be obscene'' and lack ''serious literary, artistic, political or scientific value'' - the Supreme Court's 1973 guideline on obscenity.

The NEA chairman, however, would retain authority to make final decisions on the artistic merit of grant applications.

Also, the bill earmarks $250,000 for a 12-member commission to study the NEA's grant-making process to determine whether new standards should be adopted governing federal subsidies for controversial art.

''It's certainly going to put a chill in the air, because the endowment is being asked not only to judge artistic quality but to act as a moral watchdog,'' said Martin Friedman, director of the Walker Art Center in Minneapolis.

Hoping to avoid becoming embroiled in the controversy, Washington's Corcoran Gallery of Art canceled plans to display the traveling Mapplethorpe exhibition last July, but the move backfired disastrously.

The venerable museum suffered artist boycotts, the resignation of the museum's chief curator, loss of a $1.5 million bequest from artist Lowell Nesbitt, a plunge in staff morale and a tarnishing of the Corcoran's reputation as a showcase for contemporary American art. The Corcoran trustees are studying how to repair the damage, including whether director Christina Orr-Cahall should be fired.

Frohnmayer, vacationing in Oregon late last week, said in a telephone interview that he intends to shift public attention from the Mapplethorpe- Serran o controversy to the endowment's largely overlooked ''good works'' in underwriting artistic excellence.

''We have a very fine line to walk here between continuing artistic freedom and maintaining the public trust, when you're using taxpayer dollars,'' said Frohnmayer, a former chairman of the Oregon State Arts Commission.

He rejects any notion that he'll be coming to Washington as a government censor. But he intends to find out ''how we got into this controversy in the first place, and to make sure we avoid a similar controversy in the future.''

Frohnmayer said he specifically will take steps to ensure greater NEA control over grants to local arts institutions that currently dispense the money to artists at their discretion.

The Mapplethorpe exhibition was organized by the University of Pennsylvania's Institute for Contemporary Art in Philadelphia and partially financed by an NEA grant. Serrano's works were underwritten by endowment funds awarded to the Southeastern Center for Contemporary Art in Winston-Salem, N.C.

Frohnmayer will succeed Frank Hodsoll, who departed in February, as chairman of the independent federal agency, which dispensed $156 million last year to about 800 artists and 3,800 arts institutions, from major symphony orchestras and opera companies to poets, folk artists and small-town theater companies.

Grants are awarded after an exhaustive selection process involving ''peer panel review'' of applicants by fellow artists. These panels' recommendations are subject to approval by the NEA chairman and the National Council on the Arts, the endowment's independent, presidentially appointed advisory body.

Besides putting the government's imprimatur on cultural endeavors of the highest quality, endowment officials say, the matching grants serve as a catalyst for private financial support of the arts. They estimate that every federal dollar spent in NEA grants has yielded more than $5 in contributions from individuals, corporations and foundations.

The endowment is no stranger to political controversy. It has weathered recurring congressional hearings on its grant-making process. It rebuffed allegations by conservative lawmakers a few years ago that it was subsidizing ''pornographic poetry'' and wasting taxpayers' money on projects to design a new bathtub and make clothing from sheet metal.

But Livingston L. Biddle, who drafted the legislation that created the arts endowment in 1965 and served as NEA chairman under President Carter, said ''there has been nothing in my experience like the firestorm that erupted'' over Mapplethorpe and Serrano.

Biddle is confident the Helms controversy won't inhibit the endowment's nurturing of artistic freedom, but he sees an affirmation of John Milton's warning that freedom involves responsibility.

''What has emerged is a cautionary signal to the endowment that it must be alert to difficulties that could arise from the extremely controversial,'' said Biddle.

''We're all pretty worried about censorship,'' said Deborah Butterfield, a Bozeman, Mont., sculptor who serves on an endowment oversight panel on the visual arts.

''I think it's vital to preserve the voices that threaten people like Mr. Helms,'' she said. ''The purpose of art is to make people look at things in a different way, to solve problems in a creative way. That is not necessarily comfortable for those in power.''

Richard Andrews, director of the University of Washington's Henry Art Gallery in Seattle, said the ''really diabolical effect of the Helms amendment'' will be its inhibiting influence on artists rather than endowment bureaucrats.

In closing House debate on the issue last week, Rep. Fred Grandy, R-Iowa, himself a former actor on television's ''The Love Boat,'' said he hoped his colleagues weren't getting into the business of defining ''what is good taste and what is bad taste'' in the arts.

Grandy noted mischievously that the current production of a local, NEA- supported theater includes what he called ''transvestism and implied lesbian love.''

The play, he said, is Shakespeare's ''Twelfth Night,'' appearing at the Folger Shakespeare Theater.