Have you tried disabling all extensions and restart Opera to see if there is any difference (see note below)?

Note: Download from: https://ftp.opera.com/pub/opera/desktop/49.0.2725.64/mac/ (choose Opera_49.0.2725.64_Setup.dmg)

Install Opera 49, disable all extensions, and while we are at it, go to opera://flags/ and press the ”Reset all to default” (for good measure) and then go to opera://about/ and let Opera autoupdate.

When done, restart Opera, and it will maybe autoupdate again (let Opera do this, and restart the browser again when it's done).

If the browser don't crash, try to enable your installed extensions one at the time and see if you experience any issues.

If even this will fail, and Opera keeps on crashing, we need to know what's going on. Before you take any further action, it's a good idea to backup your settings which is located at: ~/Library/Application Support/com.operasoftware.Opera/ (use Finder, and the menu ”Go -> Go to folder…” and copy/paste the line above. Hold the alt key on your keyboard and drag the folder at the left of the window title which says ”com.operasoftware.Opera” and drag to your Desktop or any other location)

1. Uninstall completely. The easiest way to do this is to use a freeware third-party application named AppCleaner, don't be fooled by similar named applications if you search on Google, most of them are adware or worse, you need to do some research first. Always download directly from the developer (not from Softtronic, MacUpdate or others), in this case: https://freemacsoft.net/appcleaner/ (i have no association with the developer)

2. When AppCleaner.app is installed in the Applications folder, launch AppCleaner. Drag the Opera.app icon to the AppCleaner window and wait a couple of seconds.

3. Press the button ”Remove”, and for good measure restart or logout. When logged in again, empty the Trash.

4. Download Opera from https://www.opera.com/computer/mac and see if it works again.

5. If Opera still crashing, a crash dialog will display asking you to send a report. Go to https://pastebin.com/ (no need to register) and copy/paste the log data (or take a screenshot like: https://i.stack.imgur.com/XVMYV.png) and post the pastebin link/or screenshot here.

You can also try Opera Beta or Opera Developer.

One general advice is to see if you have any malware which mostly comes from shady browser extensions, ”video downloaders”, ”Facebook Themes” ,”system cleaners” and so on. One of the most well known free anti malware scanners is: https://www.malwarebytes.com/mac/ and i recommend to do a scan.

Opera 50 crashed frequently, with no discernible pattern. In addition to that, the extension HTTPS Everywhere -- downloaded from Electronic Frontier Foundation -- which I had used in earlier versions of Opera, started going bad in Opera 50. Two or three times.
I just downloaded Opera 51. It has already crashed once. So we'll see. If it crashes again, I'll return to Opera 49 and try disabling auto-update.
If that doesn't work, I'll have to move on from Opera.
Thanks for the input.

defaults write com.operasoftware.Opera OPDisableAutoUpdate true

If it worked, Opera will tell you "Update checker is disabled" when you go to Opera -> About Opera.

You can find old versions of Opera at https://ftp.opera.com/pub/opera/desktop/.

Is there a specific site you see these crashes on? Note that we have released Opera 51 now, maybe that fixes your issue already?

Is there nothing? If I simply drag Opera 50 to the trash and run the installer for Opera 49, what happens then?