The American Civil Liberties Union, which touts itself as a fierce defender of fair labor standards, is in a contractual dispute with an unforeseen group: its own workers. Last month, demonstrators from the UAW Local 2110 AFL-CIO, the collective bargaining unit that represents the ACLU’s assistant legal staff, administrative assistants, and other support staff, rallied outside the ACLU’s national headquarters in New York City, protesting the nonprofit’s new contract for unionized staff and accusing the organization of violating its own employees’ rights. Among the contentious issues in the new contract are smaller wage increases and the demand that workers pay...