how to downgrade from safari 13 to 12??

MAKE SURE YOU MAKE A DISK IMAGE CLONE OR BOOTABLE CLONE OF YOUR EXISTING HD ON AN EXTERNAL HD AS A FAILSAFE!

On High Sierra I had this issue and what worked for me was to selectively restore from my Carbon Copy Cloner backup the System Folder, Library and the old version of Safari from before the Safari 13 update. I searched for folders named Safari within my User account and restored those too. All other User data was left untouched.

This may work in Time Machine too but I haven't tried it.

Use your Time Machine backup to restore to a time before you installed it.

Restore your Mac from a backup - Apple Support

Do you have a complete Timemachine from just before you upgraded Safari?

Then recover that one completely.

I was able to downgrade by reinstalling from the macOS Recovery Partition. ⌘R option worked like a charm https://support.apple.com/en-us/HT204904

You can't do a selective restore for that. If you do decide to restore you could make a copy of the files that have been overwritten and then copy them back after the TM Restore. I'd assume that TM would also keep the update from today, so you might be able to restore from that.

A complete restore, as I said. No fidling. If you make a total backup somewhere, you can find newer versions of your user files on that later on.

I tried doing this and received a message that Safari was an integral system component and could not be removed.

so I've had it with Apple for good. There you set up the browser the way you want to use it, and then Apple shoots the extensions in the browser with an update. I will shoot down Safari and use Firefox from now on. I need the Mac to work. I don't want to constantly have to deal with the operating system like a Microsoft user or Linux freak.

Apple's given competing browsers a great opportunity. Downloaded Firefox looks the same and have my extensions back.

Safari is part of the OS. So yes do a complete restore.

When I attempt to restore the previous version of Safari, I get an error message "Safari" can't be modified or deleted because it's required by macOS.

Do I have to completely restore a previous TM backup?

my concern is that in doing a complete restore other files that I have made changes to will be overwritten with the previous version.

How can I do a selective restore?

Or would doing a reinstall of High Sierra resolve my problem?

Yes, you're right, I thought you were the OP on this thread. If you decide to troubleshoot Safari 13 instead, have a look here:

Browsers Protection for Safari and Adbloc… - Apple Community

If that doesn't help then I'd suggest creating your own post. You'll get more attention that way and it will be Safari specific.

Same here, Safari13 broke the ability of adding Google accounts to `System Preferences > Internet Accounts`, therefore leaving me without Google Mail, Calendar & Contacts.

Reverting to an older Time Machine backup means I will be loosing 15 days of data, which is a significant loss.

Having the ability to revert to an older version, at least as a dev. would do no harm.

Hey apple, thank you for shutting down all my extensions! And forcing me to use Chrome as default browser, good job Apple :(

What about adding video calls support for Facebook Messenger in 2019 instead of cutting already poor functionality in Safari?