During World War I, the "brethren" allowed themselves to be drafted but were expected to refuse to bear arms. The Army sent them into combat anyway, and I would imagine that at least some did as the protagonist in this movie did, and tried to do what they could to save lives. I don't know for sure whether the Society "allowed" their people to do non-combatant work for the military or not.
During World War II, JW's who weren't granted conscientious objector or 4D (Minister) status were expected to refuse induction and accept whatever sentence was handed down. JW's were not allowed to directly support the war effort in any way. I don't recall ever hearing that "alternative service" was offered as an option at that time.
At first during Vietnam, JW's who weren't grant conscientious objector or 4D (Minister) status were again expected to refuse induction and accept whatever sentence was handed down. At some point in the 60's, "alternative service," such as working at a hospital, began to be offered to such men as an alternative to prison. For a while, young JW men were told by their elders to refuse any such offers and not to even hint that they would be willing to perform such service in lieu of going to prison. Only if actually sentenced to alternative service could a young man accept the assignment and stay in good standing with the congregation. There could be no plea bargain or "deal" beforehand. On top of that, the young men were warned to never say that the elders told them to take this stand. They had to say it was their own position and that no one had influenced their decision in any way.
In the late 60's and early 70's, when the Vietnam war began winding down, the Society quietly softened this stance and the young men were allowed to actually seek out such alternative service. No apology was ever offered to those who went to prison unnecessarily. In fact, the blanking Society had the gall to print an article practically chastising those who dared feel that they had suffered needlessly due to the whims of Society policy.
I am not aware of any support offered by the Society or any efforts at all being made to mitigate the suffering of these men or their families who sacrificed so much for the Truth™.