Seems like this is another bit of history that is kept quiet.
MARK A SITY
Up till 1948 the term "Palestinian" referred to Jews living in British Mandatory Palestine. The Arabs just called themselves Arab until the mid 60's when the PLO adopted the term to inculcate an ideology of nationalism.
During WWII the Jews in Palestine supported the British and many joined the British Armed Forces whilst the Arabs supported the Nazis believing that if the Nazis won the war that would be the end of the Jews in Palestine.
The name "Palestinians" during the WWII belonged to the Jews of Palestine, who formed a Palestinian Brigade in the British armed forces and fought together with them against the Nazis.
Arab migrants to the Holy Land have hijacked the name in the late 1960s, long after the WW2. If you mean that Palestinians, they were feverish supporters of Hitler.