SendGrid requires credentials for every login using WP
This is resolved on its own, not sure why or how but this is no longer happening.  If I find more info I will post for anyone else with the same problem.

Update: This problem came back.  It is an authentication login and it is required. It is part of the Sendgrid plugin for CiviCRM. Wrote to the developer who tells me that this plugin is incorrectly listed as CRM independent - it only works 'properly' with drupal.

The authentication is required for any access to civicrm, including public listing or event registration, etc. Hence Sendgrid Plugin is not viable for WordPress.