I am posting the Wikipedia description of the Taft-Hartley Act for clarification of "Right-to-Work" law.
Some folks apparently are under the misunderstanding that RTW law "outlaws" unions or bans union membership. Not true! Right-to-Work law simply allows each individual to decide whether or not they want to financially support a union.
The Taft–Hartley Act
Prior to the passage of the Taft–Hartley Act by Congress over President Harry S. Truman's veto in 1947, unions and employers covered by the National Labor Relations Act could lawfully agree to a closed shop, in which employees at unionized workplaces must be members of the union as a condition of employment. Under the law in effect before the Taft-Hartley amendments, an employee who ceased being a member of the union for whatever reason, from failure to pay dues to expulsion from the union as an internal disciplinary punishment, could also be fired even if the employee did not violate any of the employer's rules.
The Taft–Hartley Act outlawed the closed shop. The union shop rule, which required all new employees to join the union after a minimum period after their hire, is also illegal. As such, it is illegal for any employer to force an employee to join a union.
A similar arrangement to the union shop is the agency shop, under which employees must pay the equivalent of union dues, but need not formally join such union.
Section 14(b) of the Taft–Hartley Act goes further and authorizes individual states (but not local governments, such as cities or counties) to outlaw the union shop and agency shop for employees working in their jurisdictions. Under the open shop rule, an employee cannot be compelled to join or pay the equivalent of dues to a union, nor can the employee be fired if he joins the union. In other words, the employee has the right to work, regardless of whether or not he is a member or financial contributor to such a union.
The Federal Government operates under open shop rules nationwide, though many of its employees are represented by unions. Unions that represent professional athletes have written contracts that include exclusive representation provisions (for example in the National Football League), but their application is limited to "wherever and whenever legal," as the Supreme Court has clearly held that the application of a Right to Work law is determined by the employee's "predominant job situs." Hence, players on professional sports teams in states with Right to Work laws are protected by those laws, and cannot be required to pay any portion of union dues as a condition of continued employment.