Are you using the user registration page for the user registration full page? Both of these should redirect to the profile page after a successful registration. On the profile page is an access check to determine if the user is logged in. If the user is not then they will be redirected to the login page. This access rule is based on the presence of the following two session variables:
When you register and are taken to the login page what is in the URL bar? Are you able to login with the user after registering? Please post back with this info and also any other details you can think of.