I don't really understand why the idea of union shops bothers people.
Freedom also means you can strike, walk-out, or quit your job if you want. Union shops exist because unions have the power to have everyone else walk out if someone is hired who isn't in the union. That's how the concept was originally created. (I think the formalism around modern elections, created by Taft-Hartley, is actually strongly anti-union but that's another matter) it therefore seems odd to argue that you should be free to work in a union shop without joining the union, with all of your union co-workers forced to not walk out in response.
Or just speaking practically- a good union is democratic, and the democracy is much smaller - you can have more impact if you speak up- than the big democracy of the federal or state governments. So shouldn't taxes be a larger gripe than union dues? A portion of my taxes goes to fund all sorts of things I don't support.