Final answer:
Truman's unparalleled success amid conservative opposition to his Fair Deal efforts was the desegregation of the military through Executive Order 9981, the creation of public housing projects, and the expansion of Social Security coverage.
Step-by-step explanation:
Truman’s postwar New Deal and Fair Deal efforts faced significant challenges due to conservative opposition. However, he achieved an unparalleled success with the introduction of Executive Order 9981, which ordered an end to racial segregation in the military. Additionally, key legislation he succeeded in passing included major public housing projects in 1949 and the expansion of Social Security in 1950. Despite these achievements, the majority of his proposals, such as universal health insurance and increased federal aid to schools, were met with opposition and failed to pass.