TBH, I'm left with the impression that the combination of anti-semitism and anti-communism actually caused a degree of sympathy for Nazi Germany in certain circles abroad.
Of course, the reaction to Kristallnacht proved that it wasn't as widespread as one would think. And may well have been a reason why the "Final Solution" was kept a secret, in as much as possible.
And just to clarify that one in the context of your question of whether genocide might have been a factor. The Kristallnacht, abhorrent as it was, was not yet a proper genocide. It was disguised, in as much as possible, as riotting rather than as official state policy. The SA and SS agents involved were in civillian clothes and, well, pretty much tried to make it look like a riot. And while some 30,000 Jews were arrested, all were released afterwards, sans the IIRC 91 that were killed in the "riotting".
Don't get me wrong, even one innocent killed is too many, so I'm _not_ saying it's ok if it was "only" 91. But if the question was about genocide, that didn't yet qualify as a genocide for the western world.
The Jews in the western world... I don't think they were in a position to do much either way.
Before the "Final Solution" stupidity, Jews were actually encouraged to emigrate if they wanted to. Or probably it's more accurate that they'd face hatred and discrimination if they didn't. Hitler certainly hated them, but he seemed to basically have just wanted them removed, regardless of how. It didn't necessarily have to mean "killed". Yet.
I mean one of the plans actually considered until very late was acturally to create a Jewish state somewhere, and mass deport them there. Palestine was actually considered, though it soon became obvious that the Brits are not that quick to fold in the area. Another area considered was IIRC Madagascar, which also had the advantage of being an island.
The problem was that there was nowhere to emigrate to. The safest place for a Jew to go, and one of the very few options at all, was... Japan, an axis power. There are a few Jewish (small) communities IIRC in China and Japan since WW2, because the Japanese didn't have much of a problem with them (in spite of constant pressure from Nazi Germany to enact anti-semitic laws, I might add) and some of the Japanese leaders actually encouraged Jewish immigration.
Ironically that was a flip side of the same coin. Not all Japanese were doing it out of humanitarian considerations. A lot of Japanese had swallowed the anti-semitic propaganda hook, line and sinker. You know, that Jews end up taking over the banks and commerce, that Jews rule the USA, etc. But to some Japanese that actually sounded like a damn good idea. They actually hoped that importing a few thousand Jews would help their economy _and_ their foreign relations with the USA
But anyway, the best bet for a Jew to emigrate was Japan, not the USA or Western Europe.
So, to get to the actual point of this long roundabout rant: I have to really question how much influence those Jews actually had with their governments. I mean, I'm supposed to believe that they could do something like make their government go to war (see the post of our friend MagZ here), yet they couldn't arrange even a basic refugee camp for the Jews in Germany. Something doesn't quite add up. It seems to me more like actually they had buggerall say in what their country does.