Did any British or American Jews die in the Holocaust?

Jewish soldiers were often separated from their fellow soldiers bound for POW camps and sent to concentration camps. Jews that were from unoccupied but enemy countries were treated the same as European Jews. I have read that towards the end of the war man captured Jewish soldiers were not weeded out from the rest of their western allied POW compatriots. There are even stories of Germans being kind to their Jewish prisoners. However, this sort of thing was common throughout Germany towards the end of the war, because many Germans were trying to save their hides by having someone vouch for them. However, for the most part, American, British, French Jewish soldiers were mostly separated from their units and sent to the camps, although some slipped through the cracks and ended up in normal POW camps. Now the eastern European Jews fared far worse. There was an order at some point for German soldiers to summarily execute Jewish Soviet soldiers, Partisans, and Politruks / Commissars.

Now, what about Germany's allies?

The Italians, Romanians and Hungarians were German allies throughout the war, and at first they had no real anti-semitic policies. But as the war progressed the Nazis kind of forced their allies to at least monitor their Jews at first, then corral them into ghettos, and then send them to camps. One of the last 'havens' in Continental Europe for Jews was Hungary. But in the end, as Hungary's allegiance started to waver and Germany had to step in and help provide more troops and more weapons to a country that wanted out of the war, the Hungarian Jews were shipped off to concentration camps and death camps. Although they were some of the last Jews to be sent to the camps, they had a high death rate. Finland was not anti-Semitic and only sided with Germany because their war was with the Soviets, who invaded and stole about 1/3rd of their country's land. The Fins did not partake in the Holocaust and did not allow the Germans to perform any such acts in their country.

Now, in terms of actual policy towards non-enemy or neutral Jews I do not know of any specific laws. However, I do know of some anecdotal evidence that suggest that while they were treated like second class citizens they were otherwise allowed to remain free. They would have had to show papers constantly and wear a yellow star, but I believe they were allowed to live in Germany as long as the followed the rules specified for Jews. There is even a case of Heinrich Himmler trying to negotiate a German peace talk with Sweden and the World Jewish Congress. Himmler supposedly was cordial and treated his guests with respect... forced / fake of course (he was trying to save his own hide). And for money and art he allowed a couple thousand wealthy Jews to flee to Switzerland. Want to talk about awkward. Imagine being one of the head figures for the World Jewish Congress being invited to Berlin towards the end of the war to discuss the release of Jews from the camps and to help negotiate peace talks. That took guts!

Since American soldiers of whatever persuasion were more apt to be circumcized than Europeans, it wasn't so easy to divide out US Jewish soldiers by "the mark of Abraham" unless they had an obvious Semitic appearance and name.

I would imagine though I've not read much on the topic, that these Jews weren't treated any differently than European Jews that fell into the Nazstie grasp.

There were people taken from the channel islands