1. Don't deny Jewish history in Palestine. There's been a continuous Jewish presence in Palestine ever since the Romans destroyed Judea - and not just the descendants of Jews who stuck around after that; Jews have been making aliyah to Palestine, and specifically the four holy cities (Hebron, Safed, Tiberias, and Jerusalem), for pretty much the entire history of the Jewish Diaspora. Every time Jews got expelled from somewhere, some Jews migrated to Palestine. There was even an attempt, in the middle of the war between the Byzantines and Sasanians in the 7th century, to regain political autonomy in Palestine and reconstitute Judea under the Sasanids (it, uh, obviously didn't succeed.) This is all historical fact, but that doesn't mean any of it justifies apartheid in the modern day. Denying the history doesn't help anyone, it just makes you antisemitic.
2. Don't whitewash the Jewish population in Israel. Ashkenazim only make up about 31% of Israel's Jewish population, less if you consider that the 2019 study would have counted Bulgarian and Greek Jews as Ashkenazim, when they're in fact Sephardic. The majority of Israeli Jews are Mizrahim who were expelled from other countries in the SWANA region who wrongly blamed their local Jewish populations for the Nakba. There is an internal racial dynamic within Israel where Ashkenazim hold hegemony, and that is worth critiquing in concert with Israeli oppression of Palestinians, but just saying "Jews are white Europeans" is antisemitic and flatly wrongheaded. Jews are an ethnoreligious group whose members come from all racial backgrounds.
3. Don't invoke classic antisemitic tropes like dual loyalty, or tell Jewish Israelis to "go back where they came from". Most Israelis do not have a second passport, are not eligible for a second passport, and cannot return to wherever they or their grandparents came to Palestine from. Litvak Israelis can't return to Lithuania, their communities were destroyed by the Nazis and then paved over and replaced by the Soviets. Moroccan Israelis can't return to Morocco, they were expelled. American Israelis only make up about 5% of the Israeli population. Jews have always lived on "other people's land", the difference in Palestine is that we're the oppressor, rather than the oppressed.
4. Understand why Israelis fear the Palestinian Right to Return, even if that fear is something you (rightly) oppose. It's true that settlers always become anxious about the people whose land they stole fighting back, but with Israelis this is even more potent due to two thousand years of antisemitism, and in particular, an event in living memory. In 1932, German and Austrian Jews were stripped of their citizenship, becoming stateless, and when the Evian Conference was held in 1938 to address what to do with the Jewish refugees, all 32 countries in attendance refused to take in more than at most 30,000 Jewish refugees, and that "most" was from the USA and the UK. (Except the Dominican Republic, but that was because Trujillo wanted to bring in a surge of Europeans to overwhelm the country's Black population, so...) When my country, Canada, itself a settler colony, was asked how many Jewish refugees would be allowed into Canada after the war, the infamous response was "None is too many." Golda Meir, then representing the British Mandate in Palestine, and later a Prime Minister of Israel who said and did some awful shit to Palestinians, was not permitted to speak or participate in the conference, she was only allowed to observe as country after country refused to accept Jewish refugees in any large number. (Though it should be noted that Chaim Weizmann and David Ben-Gurion, later the first President and Prime Minister of Israel respectively, actually supported this bullshit, because they thought having nowhere else to go would drive Jewish refugees to Palestine. They were right.) Israeli settlers are terrified of becoming a minority, because they do not trust the Palestinians to be any different from the rest of the world. And again, none of this justifies Israeli apartheid, but it elucidates where the Israelis are coming from, and should inform your anti-Zionist work.
5. Be specific and precise in where your principled anti-Zionism is coming from. To say that "the State of Israel is an openly settler-colonialist venture that has displaced millions of Palestinians and continues to engage in daily human rights abuses and ethnic cleansing" is specific and precise. To say that "Zionists use the Holocaust to play victim and get whatever they want"... do you understand the difference between those two statements? And why the second one might sound like when you say "Zionists", what you really mean is "Jews"?
6. Avoid double standards. Unless you genuinely believe that all white people should be kicked out of the Americas and return to Europe, don't apply that same belief to Israeli Jews. There is no post-Israeli future in Palestine that doesn't involve Jews living there. See points 1 and 4. And just to be clear, avoiding double standards cuts both ways. There is also no just future that involves the continued apartheid and ethnic cleansing of Palestine. It's evil, fascist, and genocidal for Israeli military officials to say that for all they care Gazans can go jump into the sea.
7. For fuck's sake stop putting the Neturei Karta on my dash. The Neturei Karta are a fringe group of Litvish Haredim who split off from other Haredim in Jerusalem. They're very publicly anti-Zionist while also being visibly ultra-Orthodox, so they get a lot of attention, but they're also Holocaust revisionists who attended and spoke at a 2006 Holocaust denial conference whose other speakers included David Duke of the KKK and several outright Holocaust deniers, and their leader defended Mahmoud Ahmadinejad, a president of Iran who claimed Jews made up the Holocaust. If you want anti-Zionist Jews, there are plenty of us. Check out Jewish Voice for Peace, Independent Jewish Voices, or even the Satmar if you really want Haredim. Don't give the fucking Neturei Karta any oxygen.
8. Finally: Zionism is not a euphemism. Zionism is not "when Jews do a thing I don't like," and a Zionist is not "a Jew I disagree with/don't like". Zionism is a nationalism, and like all nationalisms, it hasn't fully delivered on the liberation it was created to provide, and it's oppressed others in the process. Zionism will never go away until the material conditions that drive Jewish nationalism - that is, global antisemitism - are addressed, and yet the Palestinian right to liberation is not and must not be contingent on the end of antisemitism. This is the fundamental problem at the core of the issue: Zionists believe Jewish safety will only come from a Jewish ethnostate with a Jewish majority, and since everywhere on Earth is populated by someone, it may as well be in Palestine, given the Jewish historical roots there. And they're wrong. They're doing horrific, evil, genocidal things in the name of Jewish safety, and they're wrong to do so. But we can condemn Zionism from an informed perspective, rather than from an ignorant one, and in doing so avoid antisemitism and strengthen our anti-Zionist work. The last thing we want to do is spread Nazi rhetoric in the name of Palestinian liberation.

Can't Take My Eyes Off You