The billboards featured a foreboding message. Taxpayer money, it said, was footing the bill for a nonprofit to traffic Somali refugees — and officials in Eau Claire, Wis., had been hiding the facts for months.

When the City Council president, Emily Berge, saw the false accusations plastered last October above a thoroughfare in this river-crossed Midwestern city, her heart sank.

“I was shocked such claims would be made,” Ms. Berge said. “It was so xenophobic, and not at all what we stand for as a community.”

Xenophobic? “Hardly,” said Matthew Bocklund, an avid supporter of former President Donald J. Trump and an activist who helped raise funds for the billboards.

The message, he said, “got people to wake up and realize what was really going on.”

The billboards marked the beginning of a searing monthslong battle in central and western Wisconsin over 75 refugees, mostly from countries in central Africa. Each one had been vetted, often for years, and then invited by the federal government to come to the United States. An evangelical nonprofit would help them settle, at least initially, in Eau Claire, a predominantly white, liberal-leaning city of 70,000, surrounded by a conservative swath of rural Wisconsin.

Standing against the resettlement: a loud protest group, dozens strong, made up in part of evangelical Christians, who said cities and states should be able to say no to refugees coming to their communities.

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