A coalition of the country’s largest business and trade groups is rallying behind two National Labor Relations Board members who have been asked to sit out a case against McDonald’s because of an alleged conflict of interest, according to a filing in the case obtained by Bloomberg Law.

The board should deny the motion by Fight for $15 attorneys against Chairman John Ring (R) and member William Emanuel (R) “because it is legally dubious and would set an unnecessary and unworkable precedent,” management-side attorneys and trade groups said in their filing.

Fight for $15 attorneys asked Ring and Emanuel...