Well, unfortunately I don't think the problem is that simple.
I've removed all privacy settings concerning edit, and it saves the profile now (on the running site).
I've also rearranged quite a lot of fields, a lot of fields has been moved from 'Hiddenfromall' to 'Adgang', have been published, but not shown on either profile or edit.
'Adgang' is 'Access' and that is not shown on the profile, but is shown on the 'Edit', it's for passwords etc.
So the fields I've moved there I've set most of them to be shown on the profile, but not on edit, so they are still hidden.
I will clone this to the test site.
If I activate 'Moderator only' on a field called cb_aktiv, it again fails to save the profile.

I've created a new test site, and if I select "Moderator Only" in Edit on the field cb_aktiv on privacy plugin, it won't save the profile again.
Did I miss a field somehow?

Hi Kyle
It's the same as the previous credentials I sent.
The test user is also available.
Thankyou so much for looking into this, I'm completely baffled at this issue.

Ah, I haven't activated the edit privacy for cb_aktiv yet.
I've set it now, it is set to only allow moderator to edit the field.
And the tab I'm changing is called 'Dykkerinfo' (Diver info).