For our CD instance (the public facing website), we need to use Azure ADB2C with OpenIdConnect for authentication. And for our Sitecore CM instance, we have to use Sitecore Identity only.

Unsuccessful login with external provider. 

When I comment it out, I am able to login to sitecore but login to the public facing site breaks.

Update 2 After commenting the code as mentioned in Update 1, I can't see ".Aspnet .Cookies" getting created. I only see ".Aspnet .ExternalCookies". How to get ".Aspnet .Cookies" ?

For our CD instance (the public-facing website), we need to use Azure ADB2C with OpenIdConnect for authentication. And for our Sitecore CM instance, we have to use Sitecore Identity only.

Unsuccessful login with the external provider. 

When I comment it out, I am able to login to Sitecore but login to the public-facing site breaks.

Update 2 After commenting on the code as mentioned in Update 1, I can't see ".Aspnet .Cookies" getting created. I only see ".Aspnet .ExternalCookies". How to get ".Aspnet .Cookies" ?

Update 3

Login Controller -

     [Authorize]
        public ActionResult Login()
        {
// other logic to get identity information from .AspNet.Cookies and create virtual user, etc
but on removing app.SetDefaultSignInAsAuthenticationType(CookieAuthenticationDefaults.AuthenticationType); this Action is not getting hit
         }