You can't disable it completely. But, there are few different things you can try:

After you hide the "All Messages" access point, right-click the wrench icon on the mail panel toolbar and remove the button.

Of course, if someone figures out how to reset the toolbar or add the button back in, they can re-enable it.

You can drag "All Messages" down to the bottom of the mail panel and then hide it or collapse it. Then, if it does get enabled, it'll be out of sight a bit.

You can close down Opera and edit index.ini in the mail folder (see help -> about Opera for the location). Change the id for category 0 from id=1600000000 to id=9600000000 for example. Then, "All Messages" will be hidden and won't show up in the list to enable it. But, if you reset the mail panel to defaults, "All Messages" will reappear.

Note also that other access points like "attachments", "mailing lists" etc. shows messages from all accounts. So, you'd have to hide them as best as you can.

Even if you do all that, when you search for a message, you can choose to search all messages which will show results from all accounts.

In index.ini, you can change the flags for all the IMAP folders you want to hide. Just look for their indexes by name. Then, for each "All messages" view etc., you'd click the "settings for this view" button on the toolbar above the message list and uncheck "show hidden". Basically, you want the flags= for each IMAP folder to include the "hide from other" bit. See for more info.

But, the downside to this is that if someone rechecks "show hidden" for a view, they'll be able to see those messages again.

Another way to do it is to create a label and in its properties set "hide these messages from other views", uncheck "apply only to new messages" and create a rule that matches all messages and set "match messages in to the IMAP account or IMAP folder that you want to hide from "All messages". Then, in the "All Messages" views, messages from that account/IMAP folder will be hidden unless "show hidden" is checked. Plus, you can right-click on the "Labels" access point header, goto "customize" and choose to hide that label you created. But, someone can unhide it if they want.

It's not a good idea to set index.ini to read only, so don't try that to prevent people from unhiding things you've hidden.

In addition to searching, "Menu -> Mail -> read" might bypass any or some of the methods above.

Now, Opera doesn't support more than one user using the same profile. Each person should have their own user account on the computer where they will then each get their own Opera profile. Each profile should only have the IMAP accounts set up that they should have access too. Each user account should be password protected. Also, users shouldn't really be sharing IMAP accounts.

If that can't be done, that's unfortunate and you'll have to find a few workarounds.

You can launch Opera with the -pd "path to folder" switch (using a different shortcut for each person that has a path to a different folder for each person) so that each person gets their own Opera profile. Then, set just the IMAP accounts the user of that profile is supposed to use. You could even hide the shortcut for the Opera that you don't want other users to use (the one that has other IMAP accounts set up that others shouldn't be looking at).

You can do the multiple profile thing by launching the installer, clicking "options", changing the "install path" to a folder (different for each Opera user) and setting "install for" to "Standalone installation (USB). In this case, no shortcuts will be created by default, but you can go into the installation folder of each and create a shortcut (no -pd switch necessary in this case as each will already be a standalone profile).

You could set up just 2 Opera profiles: one that has only the IMAP accounts that all users should have access to and another one where it also has the other IMAP accounts set up that only some users should have access to. Then, you hide that installation and shortcut and only tell users you want about the hidden shortcut.

You'd just make sure you close down the hidden Opera when you're done with it so that users don't see it.

Or, some combo of the above.

In short, the Opera that all users use shouldn't have the secret IMAP accounts set up in it.

If you have a mix of normal messages and secret messages in the same IMAP account, I have no advice in Opera's case.