The terrorist bombings directed against West Bank Arab mayors June 2 have had two immediate effects: * They have further hardened Arab attitudes in the occupied West Bank and Gaza Strip. A bitter Arab backlash is expected. This, in turn, is certain to make still more difficult the already languishing American- sponsored effort to work out some form of self-rule, or autonomy, for the territories' Palestinian population.
* They have prompted some anguished soul-searching within Israel itself. With unprecedented ferocity, Israeli has begun to hurl invective at Israeli over an issue -- the state of Israel's relations with the Palestinians -- that has never before really gripped the national conscience here despite President Carter's peace initiative.
But any possible softening of Israeli policies that may flow from this suddenly intensified internal debate is hardly likely to overtake or reverse the hardening Arab stand, say US and other officials here.
An already endangered political species, the "moderate" Palestinian on whom Washington had placed hopes for salvaging the Camp David Palestinian autonomy process, is seen as close to extinction.
Only hours after sophisticated car bombs seriously injured the Palestinian mayors of Ramallah and Nablus and endangered the mayor of Bira, one of the most indomitable of the Arab "moderates," Mayor Rashad Shawa of Gaza, resigned. A recent Israeli crackdown in the occupied territories, Mr. Shawa suggested, had helped create the climate for terrorist violence against the Palestinians.
If the strikes against the West Bank mayors spell more trouble for the already embattled quest for Palestinian autonomy, diplomats also point to possible repercussions for Washington on related policy fronts.
"President Carter," ventured one envoy, "is going to find it a lot harder to go to his European allies or to relatively moderate Arab states like Jordan and Saudi Arabia and ask for patience on his Palestinian peace strategy."
The initial US reaction to the June 2 attacks on the West Bank mayors was studiously evenhanded. The embassy in Tel Aviv -- aware that the bombings had come exactly one month after a Palestinian ambush of Jewish worshipers in the West Bank town of Hebron -- condemned the latest terror strikes as part of a "cycle of violence and counterviolence" in the occupied territories.
Israeli Prime Minister Menachem Begin also chose his words carefully. He condemned what he termed "crimes of the worst kind," ordered an urgent investigation, and pledged the culprits would be brought to trial. But he cautioned against pointing accusing fingers at anyone before a thorough investigation and the justicial process had run their course.
Accusing fingers, many of them Israeli, were pointing almost as he spoke. All were pointing at ultranationalist Jewish groups such as the Gush Emunim (Faith Bloc) settlement movement and the Kach, or Jewish Defense League, of American-born Rabbi Meir Kahane.
The accusations, not surprisingly, came largely from the more dovish fringe of Israel. But the major opposition party, the Labor Alignment, also got into the act, with one parliamentarian suggesting that Jewish extremists were "aborting the idea of coexistence with the Palestinians."
Retired Army Gen. Matty Peled broke an Israeli taboo in suggesting similarities between the June 2 bombing and the 1948 massacre of Arabs in the village of Deir Yassin by terrorists loyal to Menachem Begin.
In the end, It was Mr. Begin's perceived threat to the Jewish mainstream of the then- infant Israeli state, more than the Deir Yassin controversy, that relegated him to several decades in the political wilderness.
"A similar equation now seems to exist in Israel with groups like Kach and Gush Emunim that have literally moved beyond the law," commented a political science professor at Jerusalem's Hebrew University.
Injury of an policeman trying to defuse a car bomb intended for Ibrahim Tawil , mayor of the town of Bira, was described as a "symbol of a growing conflict within Israel, itself, over the Jewish extremists."
The question for many here is how and when this conflict might come to a head.
Although no major confrontations were reported there by sundown June 2, Mayor Tawil, still visibly trembling from his own near-assassination, cautioned that the political atmosphere had become "very serious . . . very serious, and very sad."