Final answer:
The greatest hindrance to the Republican Party's acceptance included allegations of promoting racial equality, internal divisions on the size and role of the federal government, and the challenge of selecting candidates to unite conservative and radical voters.
Step-by-step explanation:
The greatest hindrance to the acceptance of the Republican Party can be attributed to several pivotal factors throughout its history. Initially, the party wanted to end white supremacy and enact racial equality but encountered vehement opposition. The Republicans grappled with allegations that they aimed to foster racial equality, which was a contentious concept especially in the South, and although unfounded, these allegations presented significant challenges to their acceptance.
Internal divisions also posed a serious barrier, as seen during the Reconstruction era when Liberal Republicans advocated for a smaller federal role in Southern affairs, contrasting with other party members' views. Furthermore, the Republican position on economic issues, like tax cuts for the wealthy combined with cuts to social programs, often led to public outcry, as did their resistance to programs that might have helped them politically.
The selection of political candidates who could appeal to varying factions within the party was another major issue. As the Republican Party evolved, its ability to maintain a cohesive stance on key topics like Reconstruction, federal government size, and economic policy became challenging, as evidenced by the split in the party between conservative members and radical voters.