RTW in no way prevents people from organizing; it merely removes the coercion of people that don't want to be part of it (ie taking money out of their pay check).
There's nothing stopping unions from creating exclusive contracts, so that if you want union benefits you actually have to join and pay. They realize, though, that without being able to coerce people into it, they'll only get people that would make less money other wise - high performers would choose to skip the union for better pay. In a way it's a big involuntary wealth redistribution scheme.
What you are saying is, unfortunately, not true. Under the NLRA, Unions are required to represent the non-dues paying workers just as if they were members. Also note that they get the full benefit of the contracted wages, benefits, and the right to have a union representative at any discipline hearing.
Case law, from the AFL-CIO's website:
A private sector union operates under a legally enforceable "duty of fair representation," that is, the union must fairly and equitably
represent all employees..., union and nonunion. International Assn. of Machinists v. Street, 367 U.S. 740, 761 (1961). This means a union cannot discriminate or act arbitrarily toward any employee due to the nature of his relationship with the union, and all employees are equally entitled to the unions fair and vigorous representation. All members and non-members must receive the fruits of the unions bargaining wages, benefits and all other rights and protections and enjoy full access to the grievance and arbitration process that is established to redress adverse or improper actions by the employer. 29 U.S.C. § 158(b)(2); Steele v. Louisville & Nashville R.R. Co., 323 U.S. 192, 204 (1944); Bowman v. Tennessee Valley Authority, 744 F. 2d 1207, 1213-14 (6th Cir. 1984). This right to full and fair individual treatment by the union is legally enforceable in court and before the NLRB. Vaca v. Sipes, 386 U.S.171 (1967); Plumbers Local 32 v. NLRB, 50 F. 3d 29, 31-32 (D.C. Cir.), cert. denied, 516 U.S. 974 (1995).
The only reason the GOP has a hard on about Unions is because of Election funding. We did see in the last Election that the GOP backed Citizen's united victory did squat for the GOP since a lot of Democratic Candidates who won were outspent 10-1. Look no further than my Congresswoman Tammy Baldwin. 
Facebook
Twitter