They look schizo the way a double agent can appear schizo.
Israel had a unit called the Mahal, where both Jewish and non-Jewish volunteers were allowed to migrate to Israel to fight in the 1948 Arab-Israeli War including Aliyah Bet.
About 4,000 volunteers from all over the world came to fight on the Israeli side.
Mahal made up a small fraction of the Israeli forces, except for the Air Force, where they were dominant.
Mahal was disbanded after the war, and most volunteers left Israel. Some, however, made their immigration permanent and became Israeli citizens.