Comment: At the time

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At the time

I don't think much of the Western world at the time was much opposed to the killing of Jews. They were opposed to the expansionism, and the economic upset much more so than the fact that Jews were dying. In as much as the same would have been true if Muslims were the majority non Christian population in Germany, it would have likely been opposed with equally little enthusiasm by the Allies. After all, Israel was created more as a place to stash the Jews so they wouldn't 'invade' Britain as much as anything.
When the Americans and Britons involved themselves in the war "What about the Jews" was a mantra to drum up popular support more so than any moral ideology. The Muslims would have played that role just as well. Perhaps some Jewish leaders had access to Western power players that your average Muslim would not have, given the involvement of Jewish leaders in Central Banks of the Western world. That is the only angle I can see where the notion of whether Hitler was killing Jews or not would have mattered to America or Britain.
At the end of the day, the relationship between Christians and Jews vs. Christians and Muslims probably has more to do with the recent strength (and therefore major conflict) of the Muslim empire (Ottomans)than it has to do with any actual religious issue.