Employers don't have to recognize a union in Europe, employees can still join and avail of legal support or group actions by those employees that did join.
Similarly, if the majority of your workplace is in a union, you don't have to join, just don't be surprised they don't bother defending your case if you end up a victim of unfair dismissal. Your employer may be unwilling to offer you employment terms different to what the union employees get because of the overhead for them, but if you had that little leverage you probably didn't have the imaginary invididual negotiating power the anti-union crowd imagines anyway.
If unions worked like this in the US, it seems like many more people would be in favor of them.
And the problem with open shops and opt-in unions is that scabs can be found who think in terms of the short term. A company, in contrast, has the luxury of playing the long game. So, faced with union demands, a company can hire a bunch of scabs offering benefits and pay equivalent or better than the union is currently fighting for, then when the union is crushed gradually fire the scabs and replace them with new workers who are back to the square 1 the union was fighting from. And because unionizing takes effort and conviction, the new lot might not unionize. The company wins.
Multiple unions would let workers join the union alined with their interest.