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Signup/signout & 'check if signed' up are available as Rule actions/condition
But we can't move users to a certain MailChimp group yet based on a Rule Action.
This would enable us to put users in MailChimp groups based on everything that we can reach with Rules like product purchases, Role, Profile, Userpoints, Link clicked, page visited, age, site activity, etc.
This piece of code seems to contain code on how to move a member to a different MailChimp group through the Mailchimp Module (API):
and may be partly reusable
Information about what MailChimp groups are, and how they can be valuable in email marketing: