When did humans learn that the earth is not the center of the universe?.

A major provision of the Radical Republicans’ plan for Reconstruction that Southern States find most objectionable was that a former Confederate State could not be admitted to the Union unless that State included universal voting rights in it's constitution.

Explanation:

The Radical Republicans' was a plan for the reconstruction of southern states at the civil war. These plan offered opportunities to African-Americans, estabilishing that they must have the right to vote, own properties, education, among others. If these plans were not followed, the Southern states would not be readmitted into the Union

The biggest condition was universal voting rights.

So

A major provision of the Radical Republicans’ plan for Reconstruction that Southern States find most objectionable was that a former Confederate State could not be admitted to the Union unless that State included universal voting rights in it's constitution.