Alabama Republicans who are looking for an alternative to Mr. Moore are turned off by the Democrats over a constellation of issues — Supreme Court nominations, the scope of federal regulation, the fact that a Democrat would probably stymie President Trump’s agenda and the general sense that the national Democratic brand is in conflict with white Southern culture. But the obstacle that voters most commonly bring up, from the college town of Tuscaloosa to suburban Birmingham to Mr. Moore’s home county in northeast Alabama, is Mr. Jones’s stance on abortion.

“The biggest thing for me is that he’s pro-choice,” said Susan Moore, a retired respiratory therapist who said she had been unhappy with Mr. Moore (who is no relation) for years, frustrated by his flouting of the law while he was a judge. She said she admired Mr. Jones’s prosecution of the Ku Klux Klan members who helped plan the 1963 bombing of the 16th Street Baptist Church in Birmingham. But as for Mr. Jones in the Senate, she said, “I think he’s much too liberal for our state.”