Secretary of State Alexander M. Haig Jr.'s sudden resignation as war rages in the Middle East brought new apprehension to Israel's supporters here yesterday while Arab interests welcomed the ascendency of George P. Shultz to the helm of American foreign policy.

The Bechtel Group's association with Saudi Arabia while Shultz was president of that San Francisco-based international conglomerate raised questions among Israel's friends about whether the shift at the State Department will also mean a shift in the longstanding U.S. alliance with Israel.

Sen. Alan Cranston (D-Calif.), a member of the Senate Foreign Relations Committee and one of Israel's strongest defenders in Congress, said he was concerned about Shultz's "huge business ventures, through the corporation he's been active in, in Saudi Arabia," which is "waging holy war against Israel."

"I see it not only as bad news for Israel; it is bad news potentially for the cause of peace and stability in the Middle East," Cranston said after addressing the Democratic Party's mid-term conference in Philadelphia. "It may mean more bellicose American foreign policy, and more tilt to the Arabs which will not be good for our ally Israel."

Haig's surprise departure was hailed, however, by Arab Americans, who felt he was responsible for the Reagan administration's hands-off approach to Israel as it invaded Lebanon in its war against the Palestine Liberation Organization.

"We hope that this represents a basic change in American policy in the Middle East and that it signals conclusively that America does not support Israel's genocide of Lebanese and Palestinian people," said Robert D. Joseph, president of the National Association of Arab Americans.

To those on both sides of the Middle East war, the Haig resignation seemed to have clear implications, but in partisan domestic politics, the response was less well-defined. At the Democrats' convention, a cheer went up on the floor as party Chairman Charles T. Manatt announced Haig's departure, but many Democrats expressed regret because they felt Haig was a voice of moderation in the administration.

"Haig had the voice of a hawk, but his heart was approaching that of a dove," said Sen. Claiborne Pell (R.I.), ranking Democrat on the Senate Foreign Relations Committee. "Haig was a moderating influence. He relied on professional diplomats, not amateur ideologues."

Likewise, Sen. Paul E. Tsongas (D-Mass.) commented, "I'd trade Haig for the rest of them in the administration in a moment's notice. It has to be seen as a victory of the hard-liners over the moderates."

Sen. Charles H. Percy (R-Ill.) chairman of the Senate Foreign Relations Committee, whom Israel does not consider friendly, said Reagan "could not have made a better choice" in Shultz and predicted he would win swift Senate confirmation.

But a note of concern came from another senior Republican on the Foreign Relations Committee, Sen. Charles McC. Mathias of Maryland, who lamented the loss of "a voice of moderation."

That voice of moderation was what so angered many of Haig's hard-line critics in the New Right. They faulted his approach to strategic nuclear arms talks as well as his views on China and Taiwan and Latin America.

They greeted his resignation as a long-awaited fulfillment of a demand they had made of the White House for months. But their delight was dampened by uncertainty over Shultz, whom some conservatives had found even less acceptable than Haig when Reagan was making his choice for secretary of state the first time.

"Haig was virtually completely captured by the foreign-policy establishment that has run the State Department," said Paul Weyrich of the Committee for the Survival of a Free Congress. "Where he had come in pledging that he would clean house, quite the contrary. They took hold of him and really had an impact on his thinking.

"But I don't think his resignation is a victory for conservatives. Quite the contrary. Many of us supported Haig as secretary of state in an effort to prevent Shultz from getting the job," he added.

Richard Viguerie, the direct-mail specialist and New Right fund-raiser, said Haig's resignation presented Reagan with "an 11th-hour opportunity to get American foreign policy back on track," But Viguerie wasted no time in delivering a negative verdict on Shultz.

"Why must the President again turn to big business for one of his top foreign policy officials when too often these multinational companies put their own interests ahead of America's best foreign policy interests?" he asked. "These people have been the architects of the last 35 years of failed American foreign policy."

"Just because you don't like arsenic, doesn't mean you have to like cyanide," said Howard Phillips of the Conservative Caucus in describing the view of conservatives toward the former and newly designated secretaries of state.

Questions about Shultz's connection with Bechtel and his views toward the Middle East war and the U.S. alliance with Israel dominated the early reaction to his nomination. Cranston said he would bring up the Bechtel connection when Shultz's confirmation hearings begin the week of July 12.

Sen. Larry Pressler (R-S.D.), also a member of the Foreign Relations panel, said Shultz's Bechtel ties "may make things more difficult in the Mideast." Pressler said Bechtel has large contracts with the Saudis and lobbied heavily for the sale of AWACS radar planes to them--which the Senate narrowly approved last year over strenuous Israeli opposition.

Hyman Bookbinder, Washington representative of the American Jewish Committee, said he does "not attach a great deal of importance" to Shultz's relationship with Bechtel. "There will be people that will be suspicious that his Bechtel association will make it difficult for him to be objective," he said, but described Shultz as "a man of integrity."