Hi Joseph and Sophia,
I didn't know that about Judaism in general or Judaism in India, that they admit hierarchies. My exposure in India was limited to meeting a family in Kolkata, one of the 400-500 remaining Jewish Indian families in the early -mid 1980s (~150 in Kolkata and ~300 in Mumbai). My exposure in the US has been extensive (grad school in Physics), but I suspect to mostly Reform Jews or secular/atheist Jews.
I am confused by the division between Kohanim, Leviim and Yisraelim being from father to child, since as I had understood it and per https://www.jewishvirtuallibrary.org/patrilineal-descent only the child of a Jewish mother is considered Jewish. Perhaps I shouldn't be, since with these positions comes power and that is usually patrilineal.
In Parsis, the inheritance of the Parsi religious status is only to children of Parsi fathers https://en.wikipedia.org/wiki/Women_in_Zoroastrianism#:~:text=The%20children%20of%20an%20intermarriage,nor%20be%20raised%20as%20such.
To the larger question of Caste in Judaism. In her book on Caste, Isabel Wilkerson identifies "8 pillars of Caste" all of which manifest slightly differently in the three examples she considers, but all do manifest:
1. Divine will and laws of nature
4. Purity vs. Pollution
5. Occupational Hierarchy
6. Dehumanization and Stigma
7. Terror and Cruelty as enforcement and control
8. Inherent superiority/inferiority
My guess is that the division of Jews into the three classes you've described, though hierarchical, is not Casteist, it fails to satisfy 4, 6, 7, and 8.
Now, between Israeli Jews and Palestinians? I think that division fully satisfies all but #4 and #5 of the above 8 criteria for being Casteist.