Ok,
once you created the Auto Group rules, it should be enough to force a redirect on each user after login to the profile page. Once saved the user will take the proper groups according to Auto Group rules. I could help you to get this, but I need to know which are groups and how they should be assigned. This because we need to find a way to understand if an user should be redirected or not to the profile page.

A solution could be to add a "fake" new group (e.g. pending user) and assign this to all users. After this, each user that still belongs to this group is redirected and locked on the profile page until he updates profile. After saving, we could unassign "pending" group (using Auto Group) and that's all. To force redirect we could use ReDJ and create a rule to redirect logged users to the profile (the skip group option will redirect only non "pending" users).

Let me know if my idea is clear and what you think...

After your explaination I think it's easier then I thought. First let me answer to your question, Auto Group just assigns groups but doesn't create them. You should first create a Male and a Female group.

Now the solution.
Initially no user will have neither Male nor Female group assigned to him/her, so we have a clear condition to understand if redirect or not to the profile page. There is another extension of mine called ReDJ that can help us. We could create a redirection rule from ANY URL to the profile page URL and add a skip condition to skip redirection for guests, male and female groups. This should work but if you need assistance you should first clone the site so we can make some tests...

Kind regards,
Luigi