Final answer:
An accusation that could hurt the career and livelihood of an African American leader in the 1950s was opposing the integration of the U.S. Army.
Step-by-step explanation:
In the 1950s, an accusation that could hurt the career and livelihood of an African American leader was that they opposed integrating the U.S. Army. During this period in American history, racial segregation and discrimination were prevalent, and African American leaders who challenged these discriminatory practices faced backlash and threats to their careers. Supporting integration or advocating for civil rights could result in negative consequences for African American leaders at the time.