The assassination, conducted by Lehi, was not a popular move. Lehi, sometimes called the Stern Gang, had already become one of the most extreme groups in the Civil War in Palestine (preceding the 1948 Arab-Israeli War), and was not well-liked by its compatriots.

Being breakaways from the Revisionist Irgun group, which in and of itself was not really the mainstream Zionist organization (having broken away under its leader, Vladimir Jabotinsky, in the late 1920s and early 1930s), Lehi was already forming into one of the least-liked groups fighting the British. Their view that only violence would solve the question of Palestine, and that any Arab or British person was essentially a legitimate target, led them to perpetrate numerous bombings and acts that were looked down on by Zionists, Arabs, and British alike. Irgun is famous for its act in the King David Hotel Bombing, but Lehi is considered even more extreme than Irgun. Why? Because they not only did things like this, like bombing the immigration office in Haifa in December 1940, but because they typically walked their own path. Zionists saw them as a threat to their interests, an extreme group that jeopardized diplomacy and any peaceful resolution, while the Arabs saw them as the extremist enemy and the British saw them as a paramilitary resistance group that had to be put down, and put down hard.

All groups besides Lehi, for example, laid down their arms and grievances and fought the Nazis with the British. Lehi continued to believe in resistance to the British, instead. Also, Irgun and Lehi being more extreme than the more mainstream Haganah is best characterized by the fact that the Haganah only very reluctantly accepted British servicemen as acceptable collateral damage, while Irgun and Lehi (Lehi more fervently) were happy to attack the British directly.

Lehi's assassinations were not only Folke Bernadotte. They also assassinated Lord Moyne in 1944, which led to Churchill taking anti-Zionist actions in retaliation. Churchill said, for example, to the House of Commons:

"...if our dreams for Zionism are to end in the smoke of assassins' pistols and our labours for its future to produce only a new set of gangsters worthy of Nazi Germany, many like myself will have to reconsider the position we have maintained so consistently in the past."

Lehi's movements were not well-liked by many Jews around the world at the time. In many cases, Lehi was a lone actor who was condemned by the Haganah and Irgun. After the assassination, the Israeli government took this tack. Lehi units in the IDF were dissolved as best possible, and the group was declared a terrorist organization in response to the assassination itself. As some authors note, this was finally the excuse needed to shut down Lehi and Irgun once and for all, and consolidate Jewish power under the Haganah (which formed the backbone of the IDF) and the new government.

So we know that Lehi's action was not popular, was considered unnecessary and shameful, and regrettable in the extreme. We know that this wasn't a tack the Israelis wanted to take, especially under the new government, and that opposition to Lehi and Irgun, and their methods, had been popular in the groups that came to control Israel and the Zionist movement for decades (though Haganah would, in some cases, perpetrate acts like the Semiramis Hotel Bombing that would be comparable in some respects, but far more rarely).

Insofar as Yitzhak Shamir's involvement and his stature in Israel, a better example to look at would be Menachim Begin. Both, though, were prime ministers of Israel, and both were leaders in Irgun. They were originally kept far from politics, and Lehi groups had hardly gained any representation (I believe it was just one seat) in the first Knesset. The government was formed under Ben-Gurion, and stayed a Mapai (Labour)-dominated government (formed mostly with the religious parties in the coalition) until at least the early 1970s. It wasn't until Ben-Gurion's power finally started to wane around 1963 and he resigned that we saw any kind of shift in Israeli politics towards allowing Begin and Shamir to take real power, but even then it took almost 20 years to get them into the role of prime minister. Herut, the right-wing party of the times (and led by Begin at the start), had been kept out of virtually every coalition government until that point, and had failed to grow in any respect. Levi Eshkol, who followed Ben-Gurion, had not gotten along extensively with Ben-Gurion, and was aligned with Mapai as well. Following Eshkol, the power of Mapai kept it going through the Labour party until the late 1970s. Then, after all that had happened, from the 1967 war, the Yom Kippur War, the Suez Crisis...after all, that, the power of Labour was broken, and Likud began to gain prominence (right-wing).

It was here where Begin, and Shamir, managed to get their power as Prime Ministers into place. A combination of time, changing circumstances, and wars had led the war-weary public to shift their views, as well as economic changes in Israel. Ironically, Begin is regarded as one of the more peaceful prime ministers because of his negotiation of the 1979 peace treaty with Egypt. Shamir is less notable, and neither seems to have suffered any major stumbling because of their actions in 1948. That's not to say Israelis changed their views on the assassination, because they don't appear to have. Irgun and Lehi are still regarded as terrorist organizations by Israeli historians today. However, Israelis seem to have believed Begin and Shamir would simply be better leaders after so long under Labour leadership. As my grandfather told me just the other day, "It's ironic that Begin was so violent as a terrorist in 1948, and then ended up making one of the two peace treaties with an Arab country Israel has made so far". This seems to be the sentiment of Israeli writers I've read as well, and Shamir was similarly regarded, though less strongly so since he negotiated no peace treaty but he did try to do so as Foreign Minister under Begin with Lebanon. Most simply focus on Shamir's and Begin's later years, and say that they were "patriotic" in earlier ones, to avoid discussion of their activities, which many consider shameful and a problem for Israel's public image.

Hope this helps, happy to answer questions further!

Sources:

Gilbert, Martin. Israel: A History. New York: Morrow, 1998. Print.

Harms, Gregory, and Todd M. Ferry. The Palestine-Israel Conflict: A Basic Introduction. London: Pluto, 2005. Print.

Morris, Benny. Righteous Victims: A History of the Zionist-Arab Conflict, 1881-2001. New York: Knopf, 2001. Print.

Reich, Bernard. A Brief History of Israel. New York, NY: Facts On File/Checkmark, 2008. Print.

Smith, Charles D. Palestine and the Arab-Israeli Conflict: A History with Documents. Basingstoke: Palgrave Macmillan, 2010. Print.

Sprinzak, Ehud. Brother against Brother: Violence and Extremism in Israeli Politics from Altalena to the Rabin Assassination. New York, NY: Free, 1999. Print.