Zionism really only got started in 1897
er, yes, and the European settlers only started coming in large numbers to what is now the U.S. in the seventeenth and eighteenth centuries.
How long does a country have to be around in your eyes to be legitimate? Is your number arbitrary?
The major difference is that there are plenty of Palestianians still in camps across the world, while european diseases basically wiped out large amounts of the native American population. Israel is still a very new, as there are still people who are the original folks who where displaced.
That, and there are treaties now with native Americans settling the issues, even if wrongs where committed, while the Israel-Palestine conflict is still unsettled.
As a note - Deep space nine was in 1993-1999, at which point large jewish immigration was about ~60 years old, and the "Takeover with large refugee issues" ~45 years ago.
and right now, the six day war happened 44 years ago.
In star trek Cannon, the Cardi's started coming 60 years in, and then took over about 40 years of occupation.