Ok, so it's CB Privacy causing this problem. Darned, that's a rather important one for me.

I have a lot of configs set up in CB Privacy.
I'm not sure how to document them most effectively, and yes some of them are 'no edit display' for tabs.

Ok, I've gone through the tab privacy settings, and they are all set to 'normal cb' now.
I then tried reactivating it, and now I got this message when updating the profile:

SQLSTATE[42000]: Syntax error or access violation: 1118 The size of BLOB/TEXT data inserted in one transaction is greater than 10% of redo log size. Increase the redo log size using innodb_log_file_size.

If I deactivate it again, I can save the profile settings.

I don't have a text area, except small things, nothing that should give this error.
I'll try and go through each fields privacy settings, and remove them one by one to see which one is doing this.

Going through 68 fields' pricacy settings takes quite a while.
I just noticed that when I get the sql error the tabs shown differs from normal:
These are the headers before the sql error:

These are the headers after the sql error:

And it seems like the backend somehow is also affected.
When I test in the front end, and I then open a field in the backend it doesn't open up on the privacy integration as normal, but on the first tab for the field instead.
Btw. I don't see the error if I try as a CB Moderator.

I noticed in quite a few of the 'Display -> Default' does not have anything marked, not 'Same as Global', or anything else, I don't know if that matters.

I've gone through all the fields now, I have 19 privacy settings for fields as I can see it, but setting them all to normal didn't solve it.

When I look in the privacy plugin I can see that it has 3460 entries in privacy, and in blocked it has 4.

Should I try and uninstall it, and reinstall the plugin? Will that loose all the privacy settings, so I can recreate them?