Chaplains are specifically trained in multiple religious practices, and to help service members in their religious activities, even if these activities are not the chaplain's own.
This is correct. My father was an army chaplain during WW2, stationed at various posts in the Pacific Theater between 1942-1945 (including Okinawa). He was Southern Baptist, but conducted services for Methodists, Catholics, Jews, and whoever else was in his congregations. He had an official chaplain's manual that I saw, which covered specific rites and rituals for several religious affiliations. He acted as counselor, confessor, administered last rites, conducted worship services, funerals, and even weddings-- one young lieutenant married a native girl, which eventually resulted in a murder-suicide.
One of his criticisms of how clergy are presented in film though, was that unless a character was a Roman Catholic priest, they were usually played as buffoons.