You can make a valid argument that while Jews share common culture based in Judiasm,
Error #1. The Jewish people share a common culture, history and heritage which is based, only in part, on a shared and unique religion. The culture, customs and traditions exist outside and alongside the religion.
they are also a diverse population from around the world
...because they were ethically cleansed from their own historical, indigenous lands and who managed to avoid assimilate and retain their own culture, customs and traditions over the space of 3000 years in Diaspora.
who share as much if not more in some cases with those cultures than with each other.
Is there some sort of problem with having more than one cultural heritage? How is this relevant? It comes perilously close to the canard of "its just a religion" which delegitimizes the Jewish people, their identity and their history.
French Jews consider themselves French.
French Jews ARE French -- as in they are nationals of France. They also have some cultural attributes - notably language - of being French. Again, so what? This slides by the "are Jews more loyal to Israel or their country". Why would the adoption of another culture in any way change their Jewish identity. Are Palestinian Americans no longer Palestinian?
Jews from Arabicized cultures are considered Arab.
Not by the Jews themselves.
If you say a Palestinian could be dumped in Syria and no one could tell the difference...
WE are not the ones saying that. That originates with the people themselves. They do not consider themselves different from Syrians and Jordanians. They consider themselves one people. That is even evident in the various charters and basic laws.
The people here who work very hard to deny the Palestinians their identity are no different from their ideological opposites who put their energy into denying Jews their unique identity.
I disagree. There is a very great difference between denying the Jewish identity and acknowledging the emergence of the Palestinian identity at a certain place and in a certain time. Especially as this reflects the expressions of the Palestinian people themselves.
The question I have to ask is this : why do both sides view this as a zero sum equation where one sides identity has to be demolished in order to "win"?
Both sides do not view it as a zero sum equation. Only one side does that. That is why things like the withdrawal from Gaza can happen.