Not so, friend. 'Palestinians' are largely from either Egypt or Arabia. A Hamas official said as much; google it. No need to take MY word for a jot or tittle; look at the family names of most of the Arabs. They will tell you whence they come.
And there's almost no eastern European DNA in the descendants of Ashkenazic Jews. A 2001 study showed that their genome was still 3/4 Levantine with almost all the remainder being from either Greece or southern Italy.
Read some of Arafat's quotations about 'creating Palestinian nationality' or something like it. Again, feel free to google every jot and tittle.
If you want to suggest that indigeneity has an expiration date, I wouldn't go to any pow-wows, Aborigine events or luaus, Hawaiian or Maori, with that idea.
Finally, allow me to point out that the voting base (as well as a narrow majority of the country) of Likud and parties further right is largely made up of Mizrahi Jews--that is, the ones returned from elsewhere in the MENA region. And they did not 'mix' with the natives because the native's status would take a cliff-dive thereby, in both Christendom and Islam.
Do these people know something about Arabs that either the rest of us don't or are ignoring? Serious question. Think about it.