Add a Google account to macOS 10.14.6 running Safari 13.0?
Safari 13.0.1 fixes this issue.

From the release notes:


Fixes an issue that prevents signing into Google in Internet Accounts in System Preferences


To install Safari 13.0.1:

Go to System Preferences &gt; Software Update to install the 13.0.1 update. You'll need to restart your Mac after the installation for the Google authentication problem to go away.

If pressing the "Open Safari" button in the Internet Accounts pane of System Preferences fails to open Safari, open Safari yourself and the problem shoudl rectify itself. Safari does not need to be made the default browser for the system.



As of the time this was posted, September 20 2019, there was no known solution to the problem. Safari 13.0 broke the authentication workflow from System Preferences with Google account authentication if you use 2FA on your Google account.

The problem has been reported to Google and Apple via their official bug feedback channels.

Partial workaround

A partial workaround to the problem can be had for Mail.app and Notes.app if you add your Google account as a generic "Mail Account". For this to work you'll need to generate an application-specific password in your Google account and use this app-specific password with your Google email address to link the account to Mail.app and macOS.

To generate an application specific password for your Google account (from Google's official documentation):


Go to your Google Account.
On the left navigation panel, choose Security.
On the "Signing in to Google" panel, choose App Passwords. If you don’t see this option:


2-Step Verification is not set up for your account.
2-Step Verification is set up for security keys only.
Your account is through work, school, or other organization.
You’ve turned on Advanced Protection for your account.

At the bottom, choose Select app and choose the app you’re using.
Choose Select device and choose the device you’re using.
Choose Generate.
Follow the instructions to enter the App Password. The App Password is the 16-character code in the yellow bar on your device.
Choose Done.


To use this password with macOS:


Navigate to System Preferences > Internet Accounts and click the Add Other Account... at the bottom of the list
Select Mail account from the list
Fill out the fields:


Name: 
Email Address: 
Password: 

Click the Sign In button to complete the process. You'll be able to connect to Mail and Notes with this approach.


Unfortunately this approach won't work to make a Calendar connection from Calendar.app to your Google calendar.