I'm a little confused by that. You say unions are a fact of life there, but most employees aren't members? Why not?
I suspect it's similar to the UK.
Heavy industry doesn't really exist like it used to 50 or more years ago. Most people no longer work in steel mills, coal mines, automobile manufacturers and the like, the hotbeds of Unionism.
When socialism first gained power in the early to mid 20th Century, they nationalised all these types of companies - the means of production and all that - and so Unionism was fully integrated with the governmental structure as follows:
Large-scale production generated Unions, which bloc voted for Socialism, which when in power nationalised many companies, including not only big companies but also healthcare, transport, post office, water, electricity and many more, all of which were then encouraged, quite vigorously, to have a Union.
As heavy industry has scaled back over the last 40 years, it has been replaced in the job market by mainly the service sector, tourism and financial services and the like, most of which are not dominated by nor have any great history of Unionism.
Which results in the governmental structures, such as rail, healthcare and education still being very heavily entrenched in Unionism, while wider society has drifted away from them.
For example, we'll regularly still get train strikes in the UK, but you'll never see the bank's workers go on strike. So Unionism is entrenched in almost all governmental involved areas of society, but is almost non-existent in the burger flipping type areas of society.
I'm not sure what the ratio of Union workers per employed position is nowadays, but I suspect it's a lot less than it used to be, but would probably be more than you think it is.