Just curious. I'd also include libertarians in this question. If they do join what's their experience like?
Sometimes workers for certain industries and corporations are required to join unions regardless their policy beliefs. Period.
I was in a union for 5 years. I'm pretty much a Libertarian, although my ideas stray from the party line. During those 5 years the only thing the union did for me was take a cut out of my paycheck every week. It was a joke. It was because of the union that the company closed it's doors and sent 300+ people to the unemployment line. I honestly don't have one positive thing to say about that particular union. Granted, I understand that I had a negative experience and there are good unions out there. I've worked closely with the UAW for 10 years as well, and they aren't without their faults but those guys don't have it too bad. My experiences outside of unions has been much more pleasant and fair. I can't see myself going back.
You can not be required to join a union, by law. However, you may be required to contribute your fair share of the dues as the union must represent you even if you don't join and your employer must grant you all the privileges and wages negotiated by the union. In most cases the fair share amount can not be used for political purposes and may be contributed to a charity. See here.
"Do Any Republicans Join Unions?" Why do people join Unions? Should people have a choice or should it be forced upon them? Should more productive workers be paid the same as less productive workers? To answer the OP, of course Republican, Libertarians, and persons of all political persuasions join Unions, and for various reasons, sometimes due to threat of violence. I once instantly became an employed carpenter, simply by joining the carpenters union, but after 2 jobs determined that wasn't something I was cut out to be, or had the skills to do well.