First, lets me clarrify that I am trying to explain how this practise is justified in Norway, I am not arguing for or against it. Some of the justification is pure cultural traits, which you can try to understand even if you dont agree with them yourself. Also note that this is not completely non-controversal, but it seems like the current setup (where you need to log in to search, in addition to the public lists in the newspaper) has reasonable strong support.
This has also the effect of fueling envy
Yeah, I guess the same feeling can look like both "envy" and "sense of justice", depending on where you see it from. But we can't protect everyone from their feelings.
and allows employers to discriminate you if they see that you have side income (or if you don't).
I have never heard about this, and I don't really see the dynamic here. What definitely IS a effect is that it makes it a bit harder for employers to give employees with equal tasks very different salaries.
Why make all of this fuss about RGPD if private data is in the open?
Because this is seen as, at least partially, public data.
And why not include medical data as well? The "tribe" has the right to know how much each one costs, right?
No. And this is where you must just belive me when I say that this is just a truth about the cultue, most people (in Scandinavia) would not agree with argument. Your contribution is public, your weakness is private.
Let me give an example: The local kid socker team is organizing a cup, and the parrents need to help organizing, making and selling cookies, etc. This is organized through an app, where you sign up for tasks, and everyone can see what you are commiting to contribute. The same team also have an arrangement where the(small) membership fee can be waivered if you can't afford it, or you can get help buying equipment(shoes) for your kid. This is handled by you letting the trainer know in private, and he will discretely handle it.