Some abortion-rights supporters in Georgia are voting for Kemp, who has sought strict limits on abortions.

POWDER SPRINGS, Ga. — Though Karen Davenport, a retired schoolteacher who typically votes Republican, pulled the lever for incumbent Gov. Brian Kemp in Georgia’s primary on Tuesday, she said she did not share all of his political ideals. For one, she doesn’t think the government, at any level, should have a say in whether women can get abortions.

“I think it’s a personal choice,” Ms. Davenport, 59, said outside Burnt Hickory Baptist Church in Powder Springs, a suburban city northwest of Atlanta that was recently drawn into the district of Marjorie Taylor Greene, the inflammatory Republican congresswoman.

“An individual and their doctor should decide what’s best for them,” Ms. Davenport said. “It’s nobody else’s business. I wouldn’t go out and tell you what I’m doing with my health.”

Stephen Bass, a 35-year-old real estate appraiser, expressed a similar sentiment after casting a ballot for Mr. Kemp. He knew the governor had signed legislation in 2019 that seeks to ban abortions after six weeks — the bill is still being challenged in court — but Mr. Bass said it was not his place to weigh in on what women can do with their bodies.

“I’m allowed to have an opinion, but I don’t have the right anatomy to be making any decisions regarding abortion,” he said.

Cynthia Fowlkes, a retired educator and lifelong Democrat who moved to Georgia from New York a few years ago, said after voting in Powder Springs that she was “very religious,” so when it comes to determining the fate of reproductive rights, “I put it in God’s hands.”

Still, Ms. Fowlkes, 66, said she was inclined to support abortion rights. “I believe in a women’s right to determine how she wants to deal with her body,” she said, adding, “But I honestly don’t believe that politics should be part of this conversation.”