The idea of a "Palestinian state" came about in the 1960s as a result of Arafat and his new PLO movement. There was no conception of Palestinian national identity before the 1960s; the Arabs of present-day Israel/the Territories thought of themselves as Syrians, Transjordanians, or Levantines.
That's not true. Already in the Nakba, the refugees said "Palestine is lost." It's this Palestinian ethnogenesis that created the PLO, and not the reverse. But even before, there were signs of a growing Palestinian national identity, especially in the 1929 riots. This is in contrast to the situation in 1900 or so, when identity was more regional: people in Jaffa would say "I'm going to the Galilee" on the same basis they would say "I'm going to Syria."
What changed in the intervening decades was mass Jewish immigration, which led the Arabs in the area to develop a national identity attaching to the entire region that the Jews were trying to claim. I bring up 1929 because that's the first time we see the classical us-and-them nationalism on the Palestinian side: in the riots, the Palestinians treated all Jews as enemies, even ones who had been in Jerusalem and such since before Zionist immigration, who had previously had cool relations with the Zionists and warm ones with the Palestinians.
Of note, the UN Partition Plan did not split Mandatory Palestine between a Jewish state, Jordan, and Egypt; it split it between a Jewish state and an Arab state.
One lone lunatic does not mean there is an organized movement. Nobody in Israel supported that one crazy man any more than they supported assassinating Rabin.
No, actually, they did. The attack on the gay pride march followed years of threats and violence from the ultra- and national Orthodox against gay rights activists, especially in Jerusalem, which the Orthodox see as their own turf.
It was even worse with the Rabin assassination. While Rabin was in power, the settler movement protested with slogans like "with blood and fire we'll kick out Rabin." One protest, attended by then-opposite leader Bibi Netanyahu, featured a coffin for Rabin; after the assassination Bibi would claim his back was turned to it so he didn't see it, while the settler leaders who did see it would claim it was actually the coffin of Zionism, which in their view Rabin was killing. There was such a huge sentiment among certain sectors of the settler movement that Rabin should be killed that one rabbi had to publicly proclaim that no, it was not halachically permissible to
kill Rabin. Yigal Amir himself looked for rabbis who would confirm it was halachically permissible, and did find one. After the assassination happened, in several settlements people danced in the streets, before then claiming that Yigal Amir did not represent them and the state shouldn't tar an entire group just because of a single bad apple.
On the other hand, Jews have always been associated, by the demagogues of every Western nation, with Bolshevism so maybe you are right.
It gets even worse: in 1939, some Americans did not want to admit German-Jewish refugees fearing that they were Nazis.