RLCMN credits and thanks Walter Hudson for providing this summary and resource.
Unions created their own dilemma by initiating force against competitors, which include other unions or individual workers wishing to contract with employers separate from a union. Federal law enables unions to establish contracts granting them exclusive representation, meaning they are the only entity which can negotiate on behalf of employees. It is these exclusive representation contracts, not right-to-work, which obligate unions to represent non-members and those not paying dues. The solution is simple, unions can change their contacts to give up exclusive representation. Under right-to-work, the choice for the unions would come down to maintaining a contractual monopoly and enduring the resulting "free riders," or giving up their monopoly and competing in a free market for labor. In either case, all parties concerned would retain their freedom of association. Whether with exclusive representation or without right-to-work, employees do not have the freedom to choose whether or not to associate with a union.
Excerpts from "Effects of Right to Work Laws on Employees, Unions and Businesses" by John W. Cooper
Federal law allows unions the special power to create “exclusive representation” agreements with employers. If they choose to create these exclusive representation agreements, they are indeed required to represent all members, both dues paying members and free riding members alike. However, it does not appear that unions are actually required to set up these exclusive agreements (Greer, Union Representation).
Some proponents of RTW laws rightfully argue: “Nothing in federal law prevents union officials and employers from negotiating contracts in which the employer recognizes the union for its members only” (Greer, Union Representation).
Therefore, it appears that unions are not required by law to enter into exclusive bargaining agreements with their employers, and that if they wanted to they could form member only bargaining agreements in which they only represent their members, only their members are required to pay union dues, their contracts only pertain to their members, and other people are allowed to work for the employer independent of the union.