First, Right To Work and Prevailing Wage are two separate items. The Government jobs that are PW jobs are not covered by RTW.
Second, no law forces any company to accept and keep contracts with any union. Companies break contracts and hire a new work force all the time.
Third, RTW will affect skilled trades unions and hard. In skilled trades the union hall is also the job locator and puts the person with the proper skills on the proper jobsite. They also find jobs out of jurisdiction when times get hard and there are not enough jobs in home jurisdiction. Skilled trade unions also don't have seniority, they have no paid time off, there is no protection for "slackers" who can't or won't do the work. The contractor can fire or layoff anyone at any time for no reason, the only time they are held accountable is when they "fire without rehire" which means the person is not eligible to return. Then the union hall wants to know why.
A lot of your facts are biased by your political lean, but that hasn't stopped most of you from spouting them repeatedly.
No one forces anyone to join a union, people join because they want a job with a certain company to get the pay and benefits that are offered there. Or they join because they are adept in a trade and they want the pay and benefits offered by that trade. Indiana has always been a RTW state, no one has ever said you can't work somewhere. There have been non-UAW plants in this state for decades, there have been non-union construction contractors (and more of them than union) longer than anyone on this board has been alive.
So flame away, but get all the facts straight.
Let's talk about bias. You paint the unions - all of them - as saintly groups banding together for the good of the workers. You say no one forces anyone to join a union. Yet we have stories from the West Coast of 600 union workers storming a facility, unlawfully holding the security people, and trashing the facility over a labor dispute. In Missouri, at the state university, a labor relations class had a union leader who bragged to the class about busting heads of reluctant workers and how judicious use of sabotage in the workplace was a "legitimate" labor action.
The SEIU and other labor unions haven't shied away from using violence and coercion to get what they want and they hide behind the protective skirts of the NLRB when the companies who hire their workers fight back. I won't say YOU haven't got your facts straight, but I will say you haven't put all the relevant facts on the table, either.