It's frustrating, isn't it, to be able to look back in history and ask, "Why didn't they help more?" But hindsight is 20/20. I think if they'd known then what we know now, more would have been done (I'd like to hope!).
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It is not obvious what other countries could have done in practical terms.
The routine, large-scale killings started in 1941 and took place in areas that the Allies could not access easily (or at all) ...
However, they could (and should) have listened more carefully to the early reports and publicized what was going on. The Allies could have asked resistance groups to make disrupting the Holocaust a high priority. As far as is known there was only one (!) instance in the whole of World War 2 where a resistance movement held up a train transporting Jews to camps and released and hid the 'passengers'.
Many Muslim countries do not recognize Israel.Some Arabs and some other Muslims believe that the Holocaust is misused to enhance the legitimacy of Israel.Many go a stage further and find it convenient to deny the Holocaust altogether.
In the vast majority of countries, including the US and UK, there is no law against Holocaust denial. In Germany, Austria and some other countries, public denial of the Holocaust is banned on the grounds that it is tantamount to an attempt to rehabilitate the Nazis (with a view to restoring them) and on the grounds that it is a form of Jew-baiting. Please see the link.
The Holocaust would not have happened were it not for the war. The war not only promoted the conditions to produce the Holocaust, but it also provided a shroud to cover the actions produced in the Holocaust.
Prejudice affected Jews during the Holocaust because even before the Holocaust it was all around the and during the Holocaust because the Nazi's and the SS enforced it heavily. Non-Jews were affected by it because it made them look at it with a whole new perspective.
The Allied victory in Europe ended the Holocaust. Between 1933 and 1941 the US accepted about 250,000 refugees (of all kinds) from Germany. Other countries also accepted some refugees from Germany.