MAZOMANIE, Wis. — The most memorable part of Scott Walker’s run for president in 2016 was how he ended it: By dissing Donald J. Trump, his chief rival in a crowded race.

Mr. Walker, Wisconsin’s two-term governor, said he was bowing out to help “clear the field” so a “positive, conservative alternative” could emerge to Mr. Trump. The remark was self-serving — the Walker campaign was broke — but he had a point: Republicans never coalesced around an opponent to Mr. Trump, who went on to become the first Republican presidential nominee to carry Wisconsin since 1984.

Mr. Walker is still Wisconsin’s governor, still harboring national ambitions, and Wisconsin Democrats and Republicans have only grown more divided over Mr. Trump and the state’s place in national politics. Those dynamics are now on display as Wisconsin prepares for a major primary election on Tuesday: Mr. Walker’s bid for a third term is at stake; Wisconsin Democrats’ desire to deal blows to Trump Republicanism is intense; Republicans are deeply concerned about their future hold on state government; and the very identity of the state, which swings between progressivism and conservatism, feels up for grabs.

“This just wasn’t what Wisconsin was, not what it used to be,” said Sally Mather, 69, a retired social worker, who sat in the back room of a cafe in Mazomanie, a village of 1,700, last week.