This answer focuses largely on kosher food, but it's worth noting that between WWI (mentioned in a response linked in the above answer) and WWII the Jewish chaplaincy in the US military not only grew but became entrenched in the mainstream. [EDIT: further follow up reading indicated for me that while the need grew, and in some ways the infrastructure grew, the Jewish chaplaincy did not grow. In fact, there were no Jewish chaplains at all in the interwar period, with not enough Jewish soldiers to require much more than the services of civilian rabbis near US military bases. An unprecedented number of Jewish chaplains were called up in WWII, however.) Concepts of "Judeo-Christian tradition" became entrenched and rabbis were seen in the public imagination and in the battlefield as in the same category as priests and ministers, directing their attention to the same God and standing for similar ethical values. Yet, as Deborah Dash Moore notes in GI Jews, while US Navy lifeboats were stocked with Protestant, Catholic and Jewish Bibles, symbolizing the intended synergy of the three, there was also tension in that mix, as the Catholic Bible included the statement that "Jews are the synagogue of Satan" to the protest of the Jewish chaplains.

Throughout the war, the US military worked to create a Standard Operating Procedure (SOP) based on the idea of a Judeo-Christian tradition and integrating the three above kinds of chaplains, something which was easier said than done. Chaplains were meant to focus not just on people of their own faith but, when taking the mandatory self surveys, to indicate particularly what they had done for those of other faiths. Even just within Judaism, a variety of different denominational approaches had to be melded together in ways that could not satisfy everyone (for example, most chaplains were Reform rabbis, who often clashed with Conservative and Orthodox Jews). These clashes could include disagreements over how long services should be, what kinds of religious activities should be emphasized, etc, and could even include some Jews who wanted to stay "under the radar" criticizing Jews who were more open about their Judaism and "differences." This was, after all, an era fraught with antisemitism. Yet, at the end of the day, the Jewish chaplains themselves if not necessarily the GIs they served were generally able not just to overcome interdenominational differences but to work together to solve religious questions, create religious material such as an abridged prayer book, and more.

The main responsibilities of chaplains, no matter their religion, was to make sure that all religious soldiers (mostly if said religion was Christian or Jewish- not sure about other minority religions) had the facilities to be able to observe all religious rituals, particularly those indicated in the SOP (as well as various forms of religious and spiritual guidance). As mentioned in the linked post at the top, they supplied kosher food in limited amounts (mostly around the holidays) sent by the Jewish Welfare Board. Jewish soldiers often found themselves in situations with Christian chaplains who didn't know much about Jewish holidays but had been given instructions in the SOP to make sure that, for example, a seder was held- and who therefore called in the unit's Jews to make sure that they held the seder, even if those Jews weren't necessarily that observant or interested. It had to be available to them. (In the case of a seder, the JWB generally tried to send little "seder kits" to allow the seder to be just like it would be at home.)

The idea of the SOP sometimes worked better in theory than in practice. Jews, in general, as by far the minority, knew that they had to be flexible and accommodating- nearly every Christmas and Easter shift would be staffed by Jews, where available, for example. But in a stroke of irony, for example, Chaplain Roland Gittelsohn, who had been invited to speak at the interdenominational service for the military cemetery at Iwo Jima and who had prepared a speech about the ecumenical values that underlay Judeo-Christian tradition and how they include lack of discrimination, was prevented from speaking there after some Protestant and Catholic chaplains indicated their refusal to attend the event if Gittelsohn spoke. He ended up speaking at a private Jewish ceremony, which was attended by other Protestant chaplains in protest of the decision made at the main event. Occurrences like this in some ways epitomized the kinds of conflicts that could happen in a military that had to standardize something as fraught and individual as religious observance, especially with so much history behind it. Yet, overall, however many pitfalls may have occurred, the US military in general was able to provide surprisingly robust services for a relatively small minority of Jews within its ranks.