Web pages on some sites open then immediately close. Get message saying "a problem repeatedly occurred".

This seems to be similar to issues others are having after the Safari 14.1 update 4/27/2021 that was part of the Catalina 10.15.7 update and it relates to JavaScript.  

Test the following:

Turn off “Enable Javascript” in Safari: Preferences: Security 

See if this resolves the the issue loading pages  

This is not a solution since pages are only partially complete and lacks any Javascript functionality.  

I am still searching for a fix.

Bottom Line: At this point this is most likely an Apple bug/issue related to 14.1 and they need to offer a fix other than an OSX reinstall.

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

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later. 

Isolating an issue by using another user account 

If the problem is still there, try booting into the Safe Mode using your normal account.  Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer or by using the developer’s uninstall instructions. For each disable/delete, you will need to restart if you don't do them all at once. 

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

https://etrecheck.com

In addition to the above (correct) info, OS X 10.11 is really old.

If your Mac supports an upgrade to something newer, please consider it.

If you're not sure about what upgrades might be available, use the > About This Mac option in the menus, and post the model year shown for your MacBook Pro, and somebody here can then help you determine what upgrades are available.