James’s response to my post misapprehends the current state of the law in at least two ways.
First, federal labor law provides unions the right to be the exclusive representative of a bargaining unit, with reimbursement from non-members for those additional costs, when the union achieves majority status. We can characterize the Right-to-Work law in Sweeney as either (1) gutting the federally-provided right (you can be the exclusive representative but you cannot get reimbursed for it) or (2) conditioning the exercise of that right on a demand that the union pay for it. Under (1) it looks like a preemption issue and under (2) the arrangement strikes me as importantly similar to the one in Koontz v. St. Johns River Water Management Dist.
Second, unions cannot disavow exclusive representation and simply represent their own members. Only an exclusive majority representative has the right to demand and receive recognition and a seat at the bargaining table. For minority unions, an employer is not required to bargain with them at all. While the current state of affairs seems in tension with the plain language of section 7 (which gives workers the right to “bargain collectively through representatives of their own choosing”), a union that wants to represent its own members can only guarantee its right to do so by accepting exclusive-representative status.