Todd,
There is a way to toggle that setting through the /sharing/rest endpoint of your portal:
1. Navigate to your Portal's sharing endpoint: https://yourserver.yourdomain.com/yourwebadaptor/sharing/rest and log in with the built-in administrator account ("Login" link at top right)
2. Click on the Home link (top left) and then navigate to Portals > Self, then at the bottom of this page click Update under Supported Operations
3. You should see an option called "Can SignIn Using ArcGIS", set that to True, then at the bottom of the page click "Update Organization"
Edit: If you have disabled browsing to the /sharing/rest endpoint of your Portal you will need to reenable it to get through the above steps. This can be done by signing in to the /portaladmin endpoint and navigating to Security > Config > Update and set "disableServicesDirectory" to true.
This will add back the "ArcGIS" button on the login screen for the Portal Home endpoint.
I hope this helps!
-Danny