zahavasdad “What did the Charedi population in the US do when there was a draft?”
Even during the war (that tells you my age, since anyone who say “the war” is referring to World War II) – all yeshiva students were exempted. This being a war where the consequences of defeat would be very ominous both for Jews and the country – and remember that the Germans were operating in places like the coast off Long Island and they were building batteries in Brooklyn.
While there weren’t all that many Orthodox Jews in America 70 years ago, and draft boards had discretion in who they drafted, those that did serve in the army has a hard time though one should note that most people who belonged to Orthodox shuls at the time were not Shomer Shabbos and had standards of kashruth we would consider unacceptable (and those with strict standards were likely to be in yeshiva or to have a family). It should be noted that for the most part, military service in the American army correlated with a sharp decline in level of observance (which is probably why the 1950s were the “golden age” of Reform and Conservative).
While it never was an issue for Jews, America historically exempts persons who have a religious objection to serving in the military.
Most western countries consider it to be human rights violation to do otherwise.
A more interesting question would be on service of Jews in World War I, particularly in the Hapsburg’s army, where there was a fairly high level of support for service by, and accomodation of, religious Jews (remember, they were fighting the Czar who was a notorious anti-semite).