You can try the following steps to see if it helps.

1. From the iCloud System Preferences pane, uncheck the Back to My Mac checkbox to turn it off.

2. Open the Keychain Access app (in Applications/Utilities).

3. Click the "System" keychain (You'll see keychains near the upper left of the app window).

4. Make sure "All Items" is selected in the "Category" box below.

5. In the results showing to the right, look for any key whose "Kind" is "Back to My Mac key."

6. Delete the key(s), authenticating with your password to do so.

7. Back in the iCloud System Preferences pane, re-check the Back to My Mac box.

If this doesn't help, you should go to Apple's Discussion Forum since this forum is specifically targeted towards Mozilla products.

Thank you for trying. Sadly this did not solve the problem.

Howdy! I see that I'm a few months late, but I was just having this problem and thought I might offer help to others after me who run into the same issue. So, in my case, it turns out I forgot to check my script blocker, which was blocking iCloud. I use the "NoScript" addon and, once I allowed all of the proper iCloud and Apple domains, I was able to log on just fine.

Here is a link to the Apple Support Website.