In the UK, and much of Europe, there was a good response to finding accommodation for the Ukrainian refugees from Putin's war.
I remember, in the 1990's, the Kosovans who came here, until it was safe to return home.
It would not be so straightforward, because of cultural differences, but there could be some positive response, for your Palestinian family.
On the other hand we have 'the boats' issue, as is frequently discussed on GN threads.
On yet another hand, some of our parents' generation contributed to helping find accommodation for those in the kindertransport of Jewish children to our shores.
If some in the Israeli Parliament have their way, then they will all have to leave Gaza, the West Bank and anywhere in Israel.