MADISON, Wis. — Republican-backed candidates in local school board races came out as big winners in the Milwaukee suburbs that are critical for the Wisconsin GOP in statewide elections, but they had mixed results in other parts of the battleground state.

The school board elections Tuesday in Wisconsin were among the earliest nationwide this year and are the latest sign of how politicized typically nonpartisan races for local offices are becoming across the country.

A former lieutenant governor, Rebecca Kleefisch, who is now a Republican candidate for governor, took the unusual step of endorsing 48 school board candidates. Of those, 34 won including eight incumbents, based on preliminary results. The democratic governor of Wisconsin, Tony Evers, a former teacher, school administrator, and state superintendent, did not endorse in any race.

“The pattern was traditional GOP areas, the endorsed candidates did well,” an associate professor of public administration at the University of Wisconsin-Oshkosh, Michael Ford, who studies school board races, said. “Places where it’s more ideologically balanced, it didn’t seem to matter all that much.”

The chairman of the Wisconsin Democratic Party, Ben Wikler, was buoyed by the results, saying Republicans should have performed better in a year that is supposed to favor them. They needed to perform better in swing parts of the state, he said.

“What we saw last night is a sharply divided state that’s likely to come down to the wire in the fall,” Mr. Wikler said on Wednesday.

Conservative candidates picked up school board seats at Waukesha, Wausau, and Kenosha, but lost races at Beloit and the western Wisconsin cities of La Crosse and Eau Claire.

The results reinforce the idea that the goal of Republicans getting behind school board candidates in a way they haven’t in the past was to reinforce their base ahead of the midterm elections, Mr. Ford said. It also shows that key voters in Milwaukee’s suburbs, who were uncomfortable voting for President Trump, swung back and voted for conservatives in the school board races, he said.

That could be a good sign for Republicans heading into the fall, when Mr. Evers and Senator Johnson, a Republican, are up for re-election. Mr. Johnson last year talked about the importance of local elections heading into the midterm and encouraged constituents to “take back our school boards, our county boards, our city councils.”

Republicans also saw wins beyond school board races. The Republican-backed candidate for a state appeals court seat in southeastern Wisconsin, Maria Lazar, defeated a sitting judge who was appointed by Evers. And a Republican state representative, Samantha Kerkman, won the race for Kenosha County executive, replacing a Democrat.

Republicans also touted wins in other Democratic parts of the state, including winning two of three seats on the Green Bay City Council and flipping majority control of seven county boards.

Ms. Kleefisch has made education one of her top issues and said Wednesday the wins “show that Wisconsinites are fed up and want to take back control of their communities, schools and courts.”

The GOP-backed school board candidates largely focused their campaigns on the response to Covid in schools, like mask mandates and vaccination requirements, and on exerting more control over what can be taught, particularly as it relates to race, sex, and gender issues.

Ballotpedia, which tracks election data, found that there were 53 school board elections in Wisconsin in which candidates took a stance on how race is taught, how schools or districts responded to the pandemic, or school-related sex and gender issues.