More than 500 antiabortion protesters gathered on the street outside a Fairfax County medical clinic yesterday morning, singing hymns and denouncing abortions as the equivalent of the Nazis' slaughter of Jews.

"We're here because we think society is going crazy," said Roman Catholic Bishop Thomas J. Welsh of the Arlington archdiocese, who organized the protest, the largest ever at the Northern Virginia Women's Medical Center in Annandale.

There were no arrests during the two-hour demonstration at the center, which has been the focus of repeated demonstrations and arrests since its opening six years ago.

As the demonstrators stood on Prosperity Avenue near Little River Turnpike, Carol, 15, sat on the clinic's doorstep, angered by what she saw. "How can they be so righteous and certain?" she demanded. "My sister was raped and she wants it destroyed. Why should she have to suffer through another seven months of carrying that violation inside her?"

But Welsh told the demonstrators: "There are no justifiable reasons for abortion." As he prepared to lead the protesters in prayer for the fetuses about to be aborted, Welsh added, "Even if a woman has been raped, why create a secondary evil by destroying the life that has begun? Who will speak for the children?"

The Fairfax demonstrators carried signs linking abortions to the mass murders of Jews under Hitler. "Do you remember what the Germans did to the Jews, and how blacks could suffer sterilization before the sixties?" asked Margaret Rucker, a Reston housewife. "Abortion is no different from this."

Soon after the Annandale rally ended, more than 200 persons, mostly young women, assembled on the west steps of the Capitol to demand continued public financing of abortions for poor women in the District of Columbia.

The rally, sponsored by a coalition of women's rights groups, was timed in hope of influencing a joint Senate-House conference committee that is expected to meet this week to decide upon the final version of the D.C. budget for the 1980 fiscal year, starting Oct. 1.

The House has voted -- and the Senate has rejected -- a near-total ban on abortions financed by D.C. tax funds. The conference is called to resolve the dispute.

Most speakers stressed what they called a woman's right to control her own destiny and her own body. Nan Hunter, speaking for the D.C. Area Feminist Alliance, said the antiabortion move is part of a nationwide right-wing campaign. D.C. City Council member Hilda Mason (Statehood-At-Large) said the House vote was "a violation of the . . . right of the people of D.C. to control their own locally collected taxes."

The Northern Virginia rally was somber, but the rhetoric was pointed.

"We're not here for violent purposes; I think that would be counterproductive," Welsh said. "The violence is not going on outside, with us, but inside that building."

The protesters were watched by about 25 designated marshals from the Knights of Columbus, a Catholic men's organization and 36 Fairfax police, armed with riot sticks.

The demonstration came a day after an abortion clinic in Rockville that is affiliated with the Fairfax clinic was burned in what Montgomery County police said was "definitely arson."

Antiabortionists have picketed the Fairfax clinic every Saturday since its opening in 1973. Protests against the facility, which performs some 350 abortions monthly, have not always been peaceful.

The clinic obtained a federal injunction last summer against trespassing by 11 protesters. None of the 11 was among yesterday's demonstrators, according to clinic and church officials.