A long-smoldering religious dispute in Israel, fanned by the political realities of the Menahim Begin government, has cast a shadow over Jewish high holy day observances here.

The dispute revolves around the question: Who is a Jew? More precisely, the problem is whether persons converted to Judaism by Reform or Conservative rabbis in the country will be recognized as Jews by Israeli law.

Up until now they have been, despite protestations of the Orthodox Jewish establishment in Israel that conversions by the more liberal Reform and Conservative rabbis are not strictly in accord with the Halaena (ancient Jewish religious law).

The question of Jewish identity is a critical one in light of Israel's Law of Return which grants automatic Israeli citizenship and other privileges to immigrants who are Jews.

A 1970 Israeli law defines a Jew as a person born to a Jewish mother or one who has been converted to Judaism and who is not a member of another religion.

Thus, under the law of the state of Israel. Reform and Conservative converts are recognized as Jews. That status, however, is now threatened by the Begin government.

When Begin was elected last spring, the margin of victory of his Likud party was so slim that he was forced to develop a coalition with among others, the Mizrachi and Agudah parties, the two small religious parties that represent the Orthodox viewpoint.

One of the conditions laid down by the religious parties for joining the coalition was that Begin support changing the Law of Return to exclude persons converted by Reform or Conservative rabbis.

Both rabbinical and lay organizations of Reform and Conservative groups in this country, which provide the bulk of the financial support from American Jewry to Israel, reacted quiet dismay.

Last month, a delegation of four American rabbis traveled to Israel to try to reach a compromise with Israeli Orthodox leaders. They were unsuccessful.

One of the four, Rabbi Stanley Rabinnowitz of Adas Israel Congregation here deemed the issue so important that he reffered to it in his New Year message.

He took the unusual step of alluding to the controversy within the Jewish community in his Rosh Hashanah, or Jewish New Year statement which he issued as president of the 1000 member nationwide Rabbinical Assembly of American conservative Judaism.

Rabbi Rabbinowitz praised the creative unity" which he said emerged from the "diversity" of present-day Judaism.

He then warned: "This unity will be challenged by the desire on the part of the religious establishment in the state of Israel to suggest that conversions performed by non-Orthodox rabbis are of questionable validity and that marriages performed by non-Orthodox rabbis in the Diaspora (Jews outside Israel) may not be entitled to recognition as religious marriages..."

As is customary with special messages of the Assembly head, the statement was distributed nationwide by the Rabbinical Assembly's New York Office.

Elaborating on his New Year's message in a telephone interview here, Rabbi Rabinowitz stressed the delicacy of American rabbis' positions in this issue.

"What Israel does to its own people is its own business, but when it makes such decisions" as changing the Law of Return "it affects others," he said.

The irony of the situation is underlined by the fact that while the Orthodox establishment has what he termed a "monopoly" on Jewish affairs in Israel, it does not represent the majority of Israeli citizens.

The Orthodox political parties, he said, typically command "about 12 to 14 per cent of the votes" in an Israeli election.

The Conservative rabbi denied that there is any difference in the conversion process required by Orthodox rabbis or that of Conservative and Reform. "We all require immersion in water, We all require circumcision of the male and we all require instruction," he said.

Orthodox Jews view the religion of the Conservative and Reform coreligionists as "watered-down" because the latter do not hold strictly to all of the practices followed by Orthodox who accept a more literal interpretation of the Scriptures.

The bill incorporating the Orthodox-backed changes in the law of Israel regarding conversions has already been drafted. Rabbi Rabbinowitz said, and is expected to be submitted for a vote in the Knesset in November or December.

He said the four-rabbi delegation last month held a number of press conferences in Israel appealing for defeat of the measure. "We made enough noise to hope that when the vote comes it will be in our favor," he said.

Asked if he thought a new Israeli law that would exclude Reform and Conservative converts to Judaism might dry up some of the American Jewish charity dollars for Israel. Rabbi Rabbinowitz said, "I would hope not. It would make me very mad, but I hope I wouldn't react in that fashion."

He conceded, however, that a dollar backlash" is a possibility. Anybody (in the Knesset) who votes for it would have to weigh that factor."