Republican state lawmakers have introduced at least 216 bills in 41 states to give legislatures more power over elections officials, according to the States United Democracy Center, a new bipartisan organization that aims to protect democratic norms. Of those, 24 have been enacted into law across 14 states. G.O.P. lawmakers in Georgia say the new measures are meant to improve the performance of local boards, and reduce the influence of the political parties. But the laws allow Republicans to remove local officials they don’t like, and because several of them have been Black Democrats, voting rights groups fear that these are further attempts to disenfranchise voters of color. The maneuvers risk eroding some of the core checks that stood as a bulwark against former President Donald J. Trump as he sought to subvert the 2020 election results. Had these bills been in place during the aftermath of the election, Democrats say, they would have significantly added to the turmoil Mr. Trump and his allies wrought by trying to overturn the outcome. They worry that proponents of Mr. Trump’s conspiracy theories will soon have much greater control over the levers of the American elections system.