The nomination of District lawyer Judith Richards Hope to fill a crucial vacancy on the federal appeals court here is mired in politics, its fate uncertain, along with 23 other Reagan administration nominations to federal courts across the nation.

Sen. Alan K. Simpson (R-Wyo.) charged yesterday that the Democratic majority on the Senate Judiciary Committee was engaged in an "inane, banal and childish" effort to stall the nominations as the Senate heads toward adjournment. Simpson vowed to make the nomination of Hope to the U.S. Circuit Court of Appeals for the District of Columbia a "personal top priority."

The Democrats "keep saying, 'We are going to take care of this,' " Simpson said. "But as of today no hearing date has been set." He said the Senate could conceivably adjourn as early as Sept. 30.

Hope, a 47-year-old lawyer with a long Republican affiliation, was nominated by President Reagan on April 14 for the vacancy left when rejected Supreme Court nominee Robert H. Bork retired.

Democratic aides to the Judiciary Committee deny that nominations are being stalled, asserting that the committee is processing them and plans at least one more hearing before adjournment. As the Senate reconvened this week, Sen. Joseph R. Biden Jr. (D-Del.), chairman of the Judiciary Committee, returned to work after a long illness and will now determine which of the nominees is ready for a hearing, a source said. Eleven of the 24 are awaiting hearings. "He wants to move as quickly as possible," a source said.

Democratic staffers pledged to move forward, while charging that in 1980 Sen. Strom Thurmond (R-S.C.), the Judiciary Committee's ranking Republican, announced in July that he wanted to block all the pending appointments by President Jimmy Carter, including judicial nominees. Seventeen nominations to the bench were left pending when the Senate adjourned.

All sides, however, agree on one thing: just how crucial and controversial the Hope nomination is.

Since Bork's retirement last February, the influential court has been divided roughly 6 to 5 between conservatives and liberals, with conservatives in the majority. Thus the fate of the nomination is key to the philosophical future of the court, often called the second most influential in the nation because it hears cases on a wide variety of major public policy issues.

If Hope's nomination remains stalled until the Senate adjourns and Democratic presidential candidate Michael S. Dukakis is elected, he would have an opportunity to bring the court back to a 6-to-6 split. Reagan nominated six of the judges now on the court.

"You can't beat the arithmetic," said one Democratic Senate aide. "Hope's seat is a very important seat on a very important court."

The situation appeared further complicated this week when rumors circulated on Capitol Hill that Judge Spottswood W. Robinson III, a former civil rights lawyer and a prominent member of the appeals court's liberal wing, was considering retiring, thus creating another vacancy. But the rumors appeared to be untrue, at least for the present.

Robinson refused to comment, but sources said that the 72-year-old judge had considered retiring as early as this fall because of health problems, but a good report from his doctors this summer persuaded him to stay on at least through next June. After that, "it's an open question," said one source. "It depends on how he feels."

Daniel J. Popeo, general counsel of the conservative Washington Legal Foundation, said the Hope nomination is also important because "it is Ronald Reagan's last chance to put someone on . . . this critical circuit . . . . It is essential for the Republicans to run this nomination through."

Still, neither conservatives nor liberals view Hope in the conservative mold of other Reagan appointees, certainly not a philosophical heir to Bork. "What I see is an establishment Republican," said Popeo. "I don't think she would particularly offend either the left or the right."

Hope, a Harvard Law School graduate and the daughter-in-law of Bob Hope, was national cochairwoman of Lawyers for Reagan-Bush in 1984 and was general counsel for the presidential campaign of Sen. Robert J. Dole (R-Kan.).

She is one of 11 partners in the Washington office of Paul, Hastings, Janofsky & Walker, a large Los Angeles-based firm, where she is known as an expert litigator, an accomplished lobbyist and one of the firm's rainmakers, bringing in large billings, according to a lawyer who has worked with her.

One liberal lawyer who is familiar with Hope's background said that if Vice President Bush is elected president, liberals could do far worse. "The risk you have is to put in a fairly conservative nominee now, or hold out hoping a Democrat wins," he said. "There is a downside to that risk, too."