If your use case is really simple, nbro'stext.bind('<1>', lambda event: text.focus_set()) code solves the interactivity problem that Craig McQueen sees on OS X but that others don't see on Windows and Linux.
On the other hand, if your readonly data has any contextual structure, at some point you'll probably end up using Tkinter.Text.insert(position, text, taglist) to add it to your readonly Text box window under a tag. You'll do this because you want parts of the data to stand out based on context. Text that's been marked up with tags can be emphasized by calling .Text.tag_config() to change the font or colors, etc. Similarly, text that's been marked up with tags can have interactive bindings attached using .Text.tag_bind(). There's a good example of using these functions here. If a mark_for_paste() function is nice, a mark_for_paste() function that understands the context of your data is probably nicer.
If selecting text is not something you need disabling the state is the simplest way to go. In order to support copying you can use an external entity - a Button - to do the job. Whenever the user presses the button the contents of Text will be copied to clipboard. Tk has an in-build support of handling the clipboard (see here) so emulating the behaviour of Ctrl-C is an easy task. If you are building let's say a console where log messages are written you can go further and add an Entry where the user can specify the number of log messages he wants to copy.
This is how I did it. Making the state disabled at the end disallows the user to edit the text box but making the state normal before the text box is edited is necessary for text to be inserted.
Many mentioned you can't copy from the text widget when the state is disabled. For me on Ubuntu Python 3.8.5 the copying issue turned out to be caused by the widget not having focus on Ubuntu (works on Windows).
I have been using the solution with setting the state to disabled and then switching the state, when I need to edit it programmatically using 1) text.config(state=tkinter.NORMAL) 2) editing the text and 3) text.config(state=tkinter.DISABLED).
On windows I was able to copy text from the widget normally, but on Ubuntu it would look like I had selected the text, but I wasn't able to copy it.
After some testing it turned out, that I could copy it as long as the text widget had focus. On Windows the text widget seems to get focus, when you click it regardless of the state, but on Ubuntu clicking the text widget doesn't focus it.
So I fixed this problem by binding the text.focus_set() to the mouse click event "<Button>":
import tkinter
root = tkinter.Tk()
text0 = tkinter.Text(root, state=tkinter.DISABLED)
text0.config(state=tkinter.NORMAL)
text0.insert(1.0, 'You can not copy or edit this text.')
text0.config(state=tkinter.DISABLED)
text0.pack()
text1 = tkinter.Text(root, state=tkinter.DISABLED)
text1.config(state=tkinter.NORMAL)
text1.insert(1.0, 'You can copy, but not edit this text.')
text1.config(state=tkinter.DISABLED)
text1.bind("<Button>", lambda event: text1.focus_set())
text1.pack()
For me at least, that turned out to be a simple but effective solution, hope someone else finds it useful.
Disabling the Text widget is not ideal, since you would then need to re-enable it in order to update it. An easier way is to catch the mouse button and any keystrokes. So:
seems to do the trick. This is how I disabled my "line numbers" Text widget in a text editor. The first line is the more powerful one. I'm not sure the second is needed, but it makes me feel better having it there. :)