I've lurked this forum since the late 90's and I sure as heck didn't think my first post would be to P&N, that's for sure. Anyhow...
Currently (by that I mean before RTW) if you apply for and get a job at a "union shop", you are not required to join the union if you do not wish to. However, you do have to pay a reduced fee that covers the administrative costs of bargaining the contracts that are in place that you are covered under which spell out your pay, benefits, working conditions, and the like. You wouldn't get all of the rights a full union member has, like voting for leadership or ratifying a contract.
Under RTW, if you do not want to join the union, you do not even have to pay the reduced administrative fee, but you still get all of the benefits that were bargained for the members. So while the legislature is saying that it's "pro worker, not anti-union", they hope that slowly the unions will just bleed out money covering those who choose to take the benefits and not pay for them. They even turned down an amendment that would make it so if you choose not to join the union then you would not be covered under the negotiated contracts, you would have to negotiate your own deal with management.
So they are basically forcing the unions into an unsustainable business model.
Sorry about the wall of text, tl;dr, etc...