An interesting comparison. If they took in every Jew in Germany they would have been accomplices to an ethnic cleansing but would effectively have prevented an ethnic extermination. So while technically the answer would have been yes in that case it might have been a good thing anyways.
But the analogy breaks down here because (1) the UK and USA had strongly antisemitic attitudes at the time and imposed very small quotas on the number of Jews they accepted as refugees and (2) it appears that Israel is not pursuing extermination of Palestinians.
The US and UK have a checkered record with respect to accepting people fleeing the Holocaust [1].
Saving them was not an objective of the war effort and was opposed by many due to domestic anti-Semitism and ethno-nationalism (Nazism had significant open sympathy in the US at the time).
Until the political tides changed in the US/UK, both countries definitely wasted time during which many perished in the Holocaust. Mostly people watched as the Nazis killed millions. There was no public uproar to intervene while the events were happening.
It's also not clear that either country would have ever accepted millions of Holocaust refugees, even though the US certainly had the space. The creation of the state of Israel after the war in a way helped them not have to face that question.
My reading of the history is that a not insignificant fraction of early Western support for Zionism was explicitly to avoid Jewish immigration to Western nations.
That was among the secular/ethno-nationalist rationales.
But there is also a religious rationale. In fundamentalist Christianity, the re-establishment of the state of Israel to its biblically described borders is a precondition for the return of the Messiah and Judgement Day, when the same Jewish people will supposedly be given a last chance to convert ... or else. So the policy is in part rooted in the anti-Semitism of Christian eschatology.
Those ideas had strong appeal after WW2, and they are a major policy motivator of the Christian religious right-wing in the US today.
Just one minor note: these are parts of American Protestant fundamentalist Christianity, I don't think similar concepts can be found in even the more fundamentalist factions of Catholic, Orthodox, Calvinist, Lutheran, or Ethiopian Christian sects.
Yes, I don't generally include Catholicism, Orthodox, and several other Christian sects when I use the term fundamentalist Christianity (although I'm sure fundamentalists exist in any sect of any religion).
I suppose a better term would be "evangelical protestant fundamentalist Christianity", although I suspect that even there, some small number of them are not focused on politicizing Christian eschatology.
