A federal court last month ruled that the Equal Employment Opportunity Commission had violated federal law when it decreed that businesses couldn’t take account of criminal history in hiring. Judge Sam Cummings found the agency had violated the Administrative Procedure Act by failing to provide the public with notice and the opportunity to comment on its decision. It also was a self-defeating policy, in terms of preventing discrimination. “In the absence of better information,” Civil Rights Commission member Peter Kirsanow noted, “employers use race as a proxy for criminal history.”

But why didn’t the EEOC withdraw this misguided Obama-era rule on its own? Because Obama-era commissioners still run the show. The EEOC is a bipartisan commission led by five presidentially appointed members. Two seats are vacant, giving Democrats a 2-1 majority. President Trump has nominated two outstanding candidates to fill the vacancies and give the commission a 3-2 Republican majority.

Chairman-designate Janet Dhillon is a lawyer and corporate executive—the sort of woman who would be celebrated as a feminist trailblazer if she were a progressive Democrat. In fact, she’s a conservative stalwart. The other nominee, Daniel Gade, is a retired Army Ranger who lost his leg in combat in Iraq. He holds a doctorate in public policy and administration and has taught at West Point.

These nominees should be shoo-ins. But as a condition for allowing their confirmation without lengthy debate, Democrats have insisted that Mr. Trump nominate Chai Feldblum for a third term, after her current term expires in July.

Some Senate Republicans have understandably balked at confirming the very progressive Ms. Feldblum to another term. But this means that, rather than having a Republican majority on the EEOC commission, Ms. Feldblum and the other Democratic commissioner, Charlotte Burrows, are running the show. When Ms. Feldblum’s term expires in July, she could continue to serve as a holdover for months, until a replacement is confirmed or the Senate adjourns.

The Republicans who oppose making a deal are holding back what should be an era of aggressive reform at an important government agency. Employers large and small could be affected on matters ranging from religious liberty to data-collection requirements.

With an uncertain majority after November, it’s more important than ever that Senate Republicans appoint as many qualified conservative nominees as possible. The EEOC would be a good place to start.