Force existing users to complete profile after adding required fields
I fixed this with the Rules Module.

First, I set the necessary fields in the user profile as required. That fixes it for new users that want to register.

Then, a little more complex, I used the Rules module for the existing user, with the following setup:


Event: user has logged in
Actions: 

page redirect (to user/[account:uid]/edit)
show a message on the site (to clarify why the user was sent here)

Conditions:

One OR group with the following conditions:
Data value is empty (with site:current-user:field-lastname)
Data value is empty (with site:current-user:field-firstname)
etc.



This works perfectly. The only minor point is that when I add a required field, I also have to add a condition to the OR group manually.