Is Zionism inherently racist?
No. Zionism was never based on theories of racial or even cultural superiority. Zionism, was and is a movement to achieve Jewish self-determination (there are other elements as well). For most Zionists, the place for that self-determination was and is the Land of Israel.
Is there racist Zionism?
Sure, there are certainly racist versions of Zionism, if we broaden "racism" to include theories of religious-racial superiority.
Have there been racist Zionists?
Sure, but not by virtue of their Zionism. Even the attempts of certain religious Zionists to posit a metaphysical distinction between Jew and Gentile, or who suggest that the Ishmaelites have inherited their ancestor's hatred of Isaac, etc., can not be laid at the feet of their Zionism, but rather their understanding of Judaism. And, of course, there are racists everywhere. Even cultural Zionists like Magnes expressed feelings of cultural superiority towards local Arabs in his private correspondence. But that did not figure into his Zionism. He simply was an American who had spent time in Germany, and who had the cultural snobbery that infects many people. In America, German Jews didn't let Russian Jews become members of their country clubs because they viewed the latter as uncouth and vulgar. A person can be a bigot and a Zionist, but that doesn't make Zionism bigotry.
Is Zionism inherently discriminatory?
Not all forms of Zionism are, but the sort of exclusivist-ethnic-statist Zionism that emerged in Palestine was and is inherently discriminatory – even if Zionists wish to believe that it is not. They could never give convincing arguments for the distinction between favoring Jews (good) and discriminating against Arabs (bad) on the level of the state. You really can't have one without the other.
Was Zionism essentially a colonialist movement?
There are essential colonialist elements within classical Zionism, both in practice (settlements) and in mentality (feelings of cultural superiority over the natives.) But it differs from colonialism in that it is a settler nationalism that sees its task as reclaiming its ancient land.
Was Zionism essentially anti-Arab?
Zionism essentially ignored the Arabs, at least until the Arabs made it impossible not to. Zionism was not initially directed against the Palestinian Arabs; they were the "collateral damage" of the Zionist project, especially the statist Zionist project. But with time, and with the predictable and justifiable Arab resistance, anti-Arabism entered Zionism.
But didn't a Jewish state require ethnic cleansing?
That depended on the sort of Jewish state. The state that Ben Gurion envisioned would have had great difficulties without ridding itself of the Palestinian population, which it defined as hostile. It did not have enough land for the socialist pioneers, and it did not have room for the anticipated waves of immigration. Nor was anybody interested in 1948 with power-sharing. Before 1948 the Zionists told the world that a Jewish state could arise with a sizeable Arab population. The state that the Jewish Agency accepted was 40% Arab. But upon independence the State of Israel passed a law that effectively barred the return of Palestinians to their homes, and there has been an effort to keep the total number of Arabs to no more than 20%. To justify this morally, the Zionists have engaged in self-deception; they claim that the Arabs left voluntarily and had abandoned property claims and that they could not return because they were a hostile element. The Zionists didn't want to accept responsibility for the ethnic cleansing, but they were happy for it. That is true of the vast majority of Israelis, today.
Then why do people call Zionism "racism"?
Either because they use the term loosely, or they don't understand Zionism, or because racism is very bad, and if you want to delegitimize something, you throw the word "racism" at it. Thinking people, on the other hand, can realize that "Zionism" and "racism" and "colonialism" are complicated terms, and that terminological sobriety is a virtue. Something can be very, very bad without being racist or apartheid. If I say that Israeli society discriminates against Palestinian Israelis, the discrimination need not be based on racism in the technical sense. Part of it is racist; part of it is not. All of it is very, very bad.