Democrats on the Senate Judiciary Committee reacted angrily yesterday to a questionnaire that three conservative Republicans sent to a judicial nominee, in which they asked whether he believes "that a 'viable' fetus is a human being" and sought a list of his political contributions for the last 10 years.

The eight-page document, disclosed yesterday, was sent by Sens. Jeremiah Denton (R-Ala.), Orrin G. Hatch (R-Utah) and John P. East (R-N.C.) to Joseph H. Rodriguez, President Reagan's nominee for a federal judgeship in New Jersey.

It contains seven questions about the legalization of abortion. It also asks Rodriguez for his views on matters involving prayer in public schools, the right to bear arms, the Equal Rights Amendment, union power, the death penalty, affirmative action, private school tuition vouchers and school desegregation.

Democrats said yesterday that this amounted to a political litmus test. Sen. Joseph R. Biden Jr. (D-Del.) called the questionnaire "outrageous" and said he was especially upset over the questions about Rodriguez's political contributions and political activities over the last decade.

"That's like asking whether you're a Catholic, what church do you belong to, do you contribute to your church," Biden said yesterday. "What the hell have we become? What's this all about? It's crazy."

"I'm aghast that three senators would presume to do this," said Sen. Howard M. Metzenbaum (D-Ohio). "With some U.S. senators, being a conservative is not enough; you must come up to their standard of being an extreme right-wing ideologue."

The skirmish erupted during the opening round of the administration's effort to fill 114 vacancies on the federal bench, a seventh of the total. Some Democrats said they were particularly troubled because Reagan recently withdrew two other judicial nominations that ran into strong conservative opposition.

"We now see a pattern developing," Metzenbaum said. "Unless the far right is satisfied in connection with their issues, they're going to convince the president to withdraw that nominee. It's tough enough to get by the president; now you have to go through this inquisition by United States senators."

Hatch defended the questions as "fair" and "legitimate . . . . Any senator can submit questions in writing to any judge," he said.

Hatch said that a nominee's position on abortion "is a controlling question to some of our people on the committee," and that he sees nothing wrong with that. He said the Republicans want to ensure the appointment of conservative judges.

"Every administration is concerned about having judges on the bench that share their judicial philosophy," Hatch said. "If anyone thought that former president Jimmy Carter didn't have a litmus test, they're crazy."

East said the questions were "not designed to be dilatory, but simply informational." A spokesman for Denton called the questionnaire "nothing out of the ordinary."

Judiciary Committee Chairman Strom Thurmond (R-S.C.) served notice Wednesday that he does not want such questionnaires used in the future and that nominees should be questioned only during the panel's hearings.

The three senators are awaiting a response from Rodriguez, New Jersey's state public advocate, who, if confirmed, would be the state's first Hispanic federal judge.

Rodriguez, a Democrat who has been active in promoting the rights of minorities, was recommended for the judgeship by New Jersey Gov. Thomas Kean (R). A member of Kean's cabinet and former head of the state bar association, Rodriguez also has been endorsed by Sens. Bill Bradley (D-N.J.) and Frank R. Lautenberg (D-N.J.).

The Republicans indicated that they sent the questionnaire after receiving complaints about Rodriguez from New Jersey conservatives. The document asks: "Would you give your present personal position with regards to the Equal Rights Amendment? . . . . To what extent, if any, do you feel that Congress could curtail the right of the people to keep and bear wea- pons . . . . ?"

Another question asks whether "a belief in the existence of a Supreme Being" might affect the administration's position on the rights of handicapped infants.

Thurmond has delayed committee action on Rodriguez for two weeks. The Democrats praised Thurmond's handling of the matter and dropped earlier threats to hold up future nominees.

Reagan withdrew the nomination of deputy solicitor general Andrew L. Frey to the D.C. Court of Appeals last month after 13 Republican senators -- including Denton and East -- complained in a letter that he belongs to pro-abortion and gun control groups. Reagan also withdrew the nomination of New York Legal Aid Society lawyer William E. Hellerstein after complaints that he is too liberal.

Sen. Daniel Patrick Moynihan (D-N.Y.), who recommended Hellerstein along with Sen. Alfonse M. D'Amato (R-N.Y.), responded with a letter to White House counsel Fred F. Fielding, head of the administration's judicial selection panel.

"There is a word for the ideological tests for the judiciary which are seemingly now in place in the White House and the Justice Department," Moynihan said. "That word is corruption . . . . You and your associates, in the name of the president, have decided to impose a political test for federal judges of an order so extreme as to be without precedent . . . . "