You have disabled it. There is no other setting. Restart the app and/or manually stop the two processes and the start the app again.
I tried restarging the app and rebooting the system after disabling the protected mode, but the problem persists.
If I open a pdf document by double clicking it, it's opened without protected mode. If I just left click or right click it in the Windows Explorer, two reader processes are raised and the behaviour is the same as if protected mode was enabled. I believe the document is opened by Reader X to preview the document and display its thumbnail.
Maybe it's just not possible to fully disable it, but I was hoping that someone could confirm or deny it. This is very easy to reproduce.
Thank you anyway.
Here's a statement that hopefully helps or at least solves your mystery:
While Protected Mode can be disabled for PDFs viewed with the product, Adobe continues to protect you when 3rd party software invokes a Reader process; that is, Protected Mode sandboxing cannot be disabled for shell extensions. For example, when you use Windows Explorer to preview a PDF in the Preview Pane, it starts a Reader process to display the preview. In such cases, Task Manager shows that two AcroRd32.exe processes spawn and that the operation is occurring with Protected Mode enabled.
Thanks a lot, Ben. That's what I suspected though I hadn't been able to find it clearly stated anywhere.