How can I provide anonymous user to access my REST GET API without providing any auth information? The Drupal 8 REST UI configuration page asks me to select Authentication providers for GET method; otherwise, it doesn't allow me to export the REST request.

How can I provide anonymous user to access my REST GET API without providing any auth information?
You could create your own authentication provider; it could then allow anonymous users access to your resource. It is not that difficult, the only thing I found is that you have to be careful to make sure the authentication provider only applies whe you specifically want it to. Look here for a tutorial:

http://enzolutions.com/articles/2014/12/28/how-to-create-an-authentication-provider-in-drupal-8/