Final answer:
The organization closely linked to the Republican Party where blacks could exercise their new rights as citizens is the Republican National Committee (RNC), which garnered strong support from African Americans post-Civil War. The NAACP, although not directly affiliated with the Republican Party, was established in 1909 to fight for equality for minority groups.
Step-by-step explanation:
The organization closely linked to the Republican Party where blacks exercised their new rights as citizens is the Republican National Committee (RNC). After the Civil War, the Republican Party, which was founded on anti-slavery principles and led by President Abraham Lincoln, worked to provide Black people with greater legal rights. This made the party attractive to African Americans in both the southern United States, where they were newly enfranchised, and in the Northeast. The NAACP, on the other hand, was established in 1909 and played a prominent role in the fight for civil rights but was not directly affiliated with the Republican Party. It was founded by a diverse group including W.E.B. Du Bois and was instrumental in challenging segregation and fighting for the political, social, economic, and educational equality of minority groups through legal channels and grassroots activism.