This is still working like normal for me on Ver. 45.

If you restart Thunderbird with add ons disabled is there a change? You do this under the Help menu.

I just tried that and it still won't let me add emails by clicking the star, or create email lists in my address book. So weird. Do you recommend the update? Maybe I need to do that?

I really would not recommend the update yet. I would let the new version get the bugs worked out for a few weeks. I would not have upgraded from Version 38 if I was not trying to answer questions on this forum. None of the bugs that others are seeming to have have affected me luckily.

Just to be sure you are talking about the star to the right of a senders address/name when looking at a message? The star to the left of a message header does not add to the address book.

Not being able to modify an address book usually indicates corruption of the address book. I have asked another volunteer that I think has provided a solution to address book corruption in the past to take a look at this.

The usual symptom is that you can go through the motions of changing the address book, but your changes vanish the next time you open Thunderbird. Note that with the address book, even when it's working, you may not see changes until Thunderbird is closed and re-opened.

If you think this fits what is happening for you, then maybe you could try to rebuild the affected address book.

1. Select the affected address book. This must be a "real" address book, such as Personal Address Book, and not the composite "All Addresses" book.
2. Tools|Export will let you export it. Choose the option to export to an LDIF file, as this will preserve your Mailing Lists too.
3. Now you can delete the broken address book. For user-defined address books, you can delete them within Thunderbird. For the two built-in address books, you'll need to close Thunderbird and delete the corresponding data files: Personal Address Book → abook.mab, Collected Addresses → history.mab
4. If you delete either of these, Thunderbird will re-create an empty new version next time it is opened up.
5. Now use Tools|Import to import your LDIF file to a new address book. Don't call it "Personal Address Book" or "Collected Addresses" or else you'll have trouble telling which the real address book and which is the imported copy.
6. After you have imported from the LDIF file, you can move the contacts back to wherever you prefer them to be. Ctrl+a will select all, then you can drag-and-drop onto the preferred address book's icon.

Yes, the star next to the sender's name no longer turns blue (adding the address to my address book) when I click it.

Thank you for the suggested fix, Zenos! I will try it and let you know if that helps. Going to postpone the upgrade, per your suggestions, as well.