The American Jewish community - so important to the founding and survival of the state of Israel - is divided and upset after last week's elections in Israel.

Many prominent American Jew have already sent messages to Menachem Begin, the outspoken right-wing leader of the victorious Likud Party, cautioning him that American Jewry will not be able to support an intransigently hawkish policy, if that is what the next Israeli government adopts.

Rabbi Alexander Schindler, the titular leader of organized American Jewry, is currently in Israel to convey American Jews' concern about the course the new Israeli government will follow.

Not all American Jews are worried about a Begin government, however. Some express satisfaction with his hard-line approach to the Arabs.

Despite some diferences of opinion, American Jews have remained generally united in their support for Israel since that country was founded in 1942. But several Jewish leaders interviewed this week said that American Jews would split openly and bitterly if Begin and his associates insist on a hard-line policy that appears to block progress toward a peace settlement in the Middle East.

Only a few of the persons interviewed for this story would let their names be used, a sign of the sensitivities within the Jewish community. Many Jews said it was inappropriate to criticize each other or a prospective new government in Israel publicly, regardless of their personal feelings.

Others insisted that there was "no split" in American Jewry as a result of the election.

But many talked openly of a split that could develop in the future."I wouldn't be surprised if there would be a split in American Jewry over this," said Ben J. Wattenberg of the American Enterprise Institute.

Most prominent American Jews have long-standing and intense personal relationships with the leaders of the Israeli Labor Party, which was thrown out of office in last week's elections. They are less familiar with Begin and his allies and many expressed discomfiture at the thought of an entirely new Israeli regime.

Hyman Bookbinder, Washington representative of the American Jewish Committee, observed that, "By and large, American Jews and Jewish organizations have been operating on the premise for some 10 years now that for the right kind of peace . . . under the right circumstances, Israel would substantially withdraw" from occupied Arab territories seized in the 1967 Yom Kippur war.

Begin has repeatedly said that he would not give up this territory, and that he favored formally incorporating it into Israel.

"An Israeli position now that would actually rule out any withdrawal from the West Bank [of the Jordan River] would lead to serious and anguished discussions within the American Jewish community," Bookbinder said.

Others went further. A prominent Democrat with intimate connections to the Carter administration said that an intransigent Israeli policy now would mean that the American Jewish community "isn't going to be behind them very much longer."

A wealthy New Yorker who has donated heavily to the Israeli cause said many American Jews would remain loyal to Israel whatever policy it adopts but also predicted "noticeable defections from the all-out, unquestioning support" of the past if the Begin line is put into action by a new government.

Several of those interviewed speculated that Begin - or another Likud official like his deputy, Ezer Weizman, who might be named prime minister if Begin's health prevents him from taking the job - would be forced to modify their hard line if they actually take over the government.

One who took that view was White House counsel Robert J. Lipshutz, an active Jewish leader in Atlanta before coming to Washington. Lipshutz predicted that a new Israeli government will end up making "basically the same decisions" as its predecessors on important issues, because Israeli public opiiion will demand that.

Wattenberg said he had been in Israel for the recent elections, and it was obvious tha Begin's hard-line foreign policy was his biggest liability as a candidate. Wattenberg attributed Likud's plurality victory to domestic issues like those that helped elect Jmmmy Carter last November - morality in government, the restoration of traditional values and so forth.

Wattenberg was one of several sources who speculated that Begin and his associates might play a role in peace talks with the Arabs comparable to Richard M. Nixon's in the U.S. rapprochement with China. Only a hawk like Begin, they suggested, could convince the country to make a deal with the Arabs.

Others angrily disputed that comparison, saying that Begin was too committed to his hard-line position to negotiate a reasonable bargain with the Arabs.

Several sources expressed fear that an intransigent Israeli governemnt which appeared to block a Middle East peace settlement might provoke anti-semitism in the United States, and would inevitably undermine political support for the Israeli cause in Congress and the country.

Begin's strident anti-communism and his hard-line on the occupied territories (he calls them liberated territories) could easily alienate many Americans, these sources said.

Lipshutz of Carter's staff predicted that, whatever their feelings, American Jews will now be more willing to speak out publicly about Israeli policies than they have been in the past. Lipshutz said he saw a role to be played by "people of good will" in this country who want to make their views known to Israel's leaders.