I finally found a solution to this issue here. It was option 2 in Ronald P's answer.

Basically, somehow my ~/.local/share/applications/opera.desktop file got messed up:

[Desktop Entry]
Encoding=UTF-8
Version=1.0
Type=Application
Name=(72) Facebook - Opera
Icon=opera
Exec=/usr/lib/x86_64-linux-gnu/opera/opera
StartupNotify=false
StartupWMClass=Opera
OnlyShowIn=Unity;
X-UnityGenerated=true
MimeType=x-scheme-handler/unknown;x-scheme-handler/about;x-scheme-handler/https;x-scheme-handler/http;text/html;

Adding %U to the end of the Exec= line fixed it. (And, of course, I got rid of "(72) Facebook - " in the Name= line. How the heck did this happen??? Dunno, but this is how to fix it in case anyone else has this problem. Man, I tolerated this problem for MONTHS! Glad it's finally fixed.

Yes, Thunderbird, but it also happens when opening a link from the terminal. This is why it seems like definitely an Opera problem.

Upgraded to Opera 42.0.2393.94, and it's still happening. Why? This is so weird. What can be done to fix it?

I deleted /usr/share/bash-completion/completions/opera completely now, and Opera behaves the same: links clicked in an email and the terminal still just bring up an empty (i.e. speed dial) tab.

Any help?

That would be very strange as I haven't used Opera 12 on this computer. Could it be that when I copied over my ~/.config/opera/ directory something from Opera 12 came over from way back when I did??? And then this something caused a change in /usr/share/bash-completion/completions/opera that persisted even after I purged and reinstalled Opera from scratch???

I see. Thanks for the info. I did a "find . -iname opera" on /usr, and came up with: "/usr/share/bash-completion/completions/opera". Is this the script you're talking about?

If the problem is in this script, though, wouldn't this be a widespread problem? I'd think something like that would have been reported and fixed already. Regardless, it'd be good to investigate this angle, so I'm wondering if you could post your script or suggest any changes to mine?

My Opera bash-completion script:

# opera(1) completion                                      -*- shell-script -*-

_opera()
{
    local cur prev words cword
    _init_completion || return

    case "$prev" in
        ?(-)-widget|?(-)-urllist|?(-)-uiparserlog|?(-)-uiwidgetsparserlog|\
        ?(-)-profilinglog)
            _filedir
            return
            ;;
        ?(-)-[psb]d)
            _filedir -d
            return
            ;;
        ?(-)-remote)
            COMPREPLY=( $( compgen -W 'openURL\\( openFile\\( openM2\\(
                openComposer\\( addBookmark\\( raise\\(\\) lower\\(\\)' \
                -- "$cur" ) )
            [[ $COMPREPLY == *\( ]] && compopt -o nospace
            return
            ;;
        ?(-)-windowname)
            COMPREPLY=( $( compgen -W 'first last opera{1..9}' -- "$cur" ) )
            return
            ;;
        ?(-)-geometry|?(-)-window|?(-)-display|?(-)-urllistloadtimeout|\
        ?(-)-delaycustomizations|?(-)-dialogtest|?(-)-inidialogtest|\
        ?(-)-gputest)
            # argument required but no completions available
            return
            ;;
    esac

    if [[ "$cur" == -* ]]; then
        COMPREPLY=( $( compgen -W '$( _parse_help "$1" -help )' -- "$cur" ) )
        [[ $COMPREPLY == *= ]] && compopt -o nospace
        return
    fi

    _filedir '@(?([xX]|[sS])[hH][tT][mM]?([lL]))'
} && complete -F _opera opera

# ex: ts=4 sw=4 et filetype=sh

I googled "opera startup script" but didn't find anything. @sgunhouse, I assume you're talking about an Opera startup script, as I can't see what my Ubuntu startup script would have to do with how Opera accepts a clicked link and opens it. Can you (or anyone else) tell me more about this startup script or have any other advice as to how I might fix my problem?

Which startup script?

I just discovered that this problem also occurs when opening a link from the terminal, so it must be an Opera problem.

I installed a fresh copy of Ubuntu 16.04 on an HP 280 (Intel Core i3-4170 cpu, 3.8 gigs ram, 64-bit), copied over my home directory from backup which included the ~/.config/opera/ directory, installed Thunderbird and Opera (among other programs), and now clicking links in emails causes Opera to only open a new empty tab (i.e. the speed dial).

I did a sudo apt purge opera-stable, moved .config/opera to .config/opera.old, installed Opera 42.0.2393.85 via a freshly downloaded .deb file, and still the links opened only an empty tab.

I changed my default browser to Firefox, and clicking the links in an email work.

I then changed the default browser back to Opera, and they open an empty tab again.

How can I make Opera work again?