Re: Irish republicanism
There is quite a lot of similarity between the two movements, current antagonism aside. Language revival being the most commonly noted. IDK what you would consider "principles of," but they're both nation state ideologies of the time... as opposed to republican universalism (a la france) of previous centuries.
It is also true that ireland was segregated along religious/national lines, and that protestants in ROI (I am catholic-jewish-atheist, as the old joke goes) are nonexistent today. They were about 25% before independence. Driving out protestants is emphatically not a principle of irish republicanism. Many/most founders of Irish Republicanism were, in fact, protestant. Most emigrated, moved north or converted in the generation following independence. There is some dark, rarely mentioned parts of our history of that time.
I'll also note that driving out arabs is emphatically not a principle of zionism, never was. The coming of the nation state had other ideas. zionism started in the ottoman period, and aspired to cultural autonomy of a kind that was practiced there. A nation state goal was adopted after France and Germany decided this was the future of the region.
People seem to forget how mixed Europe was before the wars, before nation states. Poland was about 50% polish. Jews, Germans and other minorities made up the rest. Its now 99% Polish-catholic. My grandfather's region (now eastern Slovakia) were Slovaks, Jews, Czechs and Ukrainians in a "majority-minority" mix. Now 99% Slovak. All of mainland europe shares this history.
When the Ottoman empire fell, giving way to nation states, same. Greek & Turkish ethnic "exchange." The Syriac & Armenian genocide. Yugoslavia & multiethnic arab countries segregated more recently. India, despite Gandhi's efforts. Etc. Empires were more multicultural than the current states.
I'll note that the philosophical distinction between universalism and ethno nationalism is barely noticeable in actual history.
Re: racial & ethnic separatism
Seeing independence as synonymous with racial & ethnic separatism is a leap. But, as I said, but if it applies to Israel it applies to half the world. In Israeli law, now and since founding, there is no preference or limits on any citizen. The only preferential law is the right of return. Actual discrimination, especially during wars, is a real thing. It is a failure though, not an ideal.
Rhodesia practiced apartheid and only allowed whites to vote. Israel never practiced apartheid, and all citizens can vote.
During the 1948 war about >1m palestinians became refugees, most ending up in the Jordanian or Egyptian parts of Palestine. >1m european jewish refugees arrived from europe and >1m arab-jewish refugees who were forced out of various countries. Thats how the demographics came to be. There was never a time when israel, as an independent state, had a jewish minority.