Mr. Kemp’s pivot has been both stylistic and substantive, and it comes as Ms. Abrams, 44, a Yale Law School graduate and former state house minority leader, has been campaigning around Georgia arguing, with wonkish delight, that her progressive policy ideas — including robust investment in public education, gun control and the expansion of Medicaid under Obamacare — amount to mainstream common sense. Her campaign calls it an “opportunity” agenda, and believes it will resonate more widely than the hot-button conservative agenda that Mr. Kemp is still known for that focuses on issues like illegal immigration and the Second Amendment.

Ms. Abrams is also hoping to appeal to moderate voters, placing decidedly more emphasis on her plans to create jobs and invest in education than her criticism of some Confederate memorials, which she has modulated recently.

On policy, Mr. Kemp, 54, Georgia’s secretary of state, recently made a small but important tweak to his longstanding promise to sign a state version of a federal religious freedom law, a possibility that frightens many in the Atlanta business community who fear that it could prompt harmful boycotts and backlash from liberals who believe such a law would be used to discriminate against the lesbian, gay bisexual and transgender community.

Various iterations of a similar state law have been promoted by Georgia conservatives in recent years as a way to protect people of faith from being forced to engage in practices they deem contrary to their beliefs. In 2016, Nathan Deal, the current governor and a Republican, vetoed a religious freedom bill that did not exactly mirror the federal law, pleasing some of Georgia’s most powerful corporations.