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A Republican backlash against George Stephanopoulos, the public face of ABC News and the network’s top political anchor, was beginning to build on Thursday after the disclosure that he had made large contributions to the Clinton Foundation in recent years.

Senator Rand Paul of Kentucky, who is seeking the Republican nomination for president, said that the donations and Mr. Stephanopoulos’s close ties with the Clintons should preclude him from moderating any debates in the 2016 presidential campaign.

“It’s impossible to divorce yourself from that, even if you try,” Mr. Paul said. “I just think it’s really, really hard because he’s been there, so close to them, that there would be a conflict of interest if he tried to be a moderator of any sort.”

Mr. Paul’s remarks, made in an interview with The New York Times, followed reports by The Washington Free Beacon and Politico that Mr. Stephanopoulos had given $50,000 to the Clinton family’s foundation since 2013.

The news seemed certain only to deepen distrust of Mr. Stephanopoulos in conservative circles, where he is viewed warily because of his longstanding personal and professional ties with Bill and Hillary Rodham Clinton. He was a senior aide in the Clinton White House during Mr. Clinton’s first term and a top strategist on the former president’s 1992 campaign.