GRAND TETON NATIONAL PARK, Wyo. — Liberal activists who stage an annual protest in favor of lower interest rates at the Federal Reserve’s annual conference here are planning a different kind of demonstration this year. They plan to don “Yellen wigs” on Friday to demonstrate in support of Janet L. Yellen, the Fed chairwoman, whose first term ends in February.

President Trump must soon decide whether to renominate Ms. Yellen or pick someone similarly inclined to emphasize economic growth. Or, instead, he could accede to the wishes of many conservatives for a Fed chairman more worried about inflation.

The looming decision is injecting an element of uncertainty into monetary policy after years of relative stability. Ms. Yellen continued the aggressive economic stimulus campaign that was launched by her predecessor, Ben S. Bernanke, during the financial crisis that began 10 years ago, and she has moved slowly to end it.

Gene B. Sperling, the former director of President Barack Obama’s National Economic Council, said the choice was a “fascinating test” for Mr. Trump, pitting conservative ideology against “the stark reality of politicians worried about how the economy performs.”