safari won't open; keep getting "safari quit unexpectedly" message

Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

Etrecheck – System Information

Do a backup, preferable 2 separate ones on 2 drives. Boot to the Recovery Volume (command - R on a restart). Run Disk Utility and select First Aid. Then re-install the OS.

Reinstall from macOS Recovery

OS X Recovery

If you want to, you can send Apple feedback. They won't answer, but at least will know there is a problem or a suggestion for change. If enough people send feedback, it may get the problem/suggested change solved sooner.

Safari Feedback

I mean... seriously? That's wrong. I shouldn't have to nuke my system. This is clearly something that Apple should fix with an update to Safari. Many people are reporting it with the new 13.0 Safari. Should be fixed by Apple.

Same problem. Crashes in other users and in Safe Boot also. Safari 13 just doesn't work for me.