How to disable PDF editing in Preview app?

According to me, the best way to resolve this, is to go to System Preferences -> General. Make sure "Ask to keep changes when closing documents" is selected.

This will prevent accidental changes in PDF files, as well as other files when opened by other apps.

Rectangular Selection Tool

A pretty poor solution to this is change the selection mode from Text Selection to Rectangular Selection in the Tools menu.

This stops you inserting random text fields, but also prevents you from selecting text, which may be equally annoying.

Locking the Document

If the document has been saved*, you can lock it...

* (there is a state for temporary files, e.g. email attachments you've opened directly from the email in Apple's Mail.app, where they are aware they're a temporary file, so pressing Save opens up a Save As dialog, and you cannot lock the document)

However, while this prevents you from editing it, if you now click in one of those places that results in a new text field, you get a rather annoying pop-up dialogue asking if you want to unlock or duplicate the document:

So this too is not an ideal solution, because it interrupts you perhaps even more than the inadvertent-text-entry-box, but technically prevents you from editing it if the Dropbox sync or similar is the main concern.

Apple Feedback

I suspect there isn't a simple way of disabling/re-enabling the auto-form-filling features of Preview (which are amazing when you want them!), so would suggest you send feedback to Apple on this one.