The short answer is:
While standard integration tools can sync Mailchimp group membership to HubSpot using custom properties, they often rely on intermittent polling and can miss real-time unsubscribe events, leading to a delay or inconsistency in your data.
The best solution for real-time, bidirectional accuracy is to use a direct, custom connection built on the HubSpot API and the Mailchimp API.
This allows you to set up immediate webhook notifications from Mailchimp whenever a subscription status or group membership changes, ensuring that HubSpot is updated instantly and accurately reflecting both additions to “Red Mail” or “Blue Mail” and, critically, immediate removals upon unsubscribing 
The long answer is:
The suggestions to use custom properties and third-party tools are valid ways to achieve your goal, but they often rely on scheduled synchronization, which means HubSpot’s data is perpetually minutes or hours behind the actual status in Mailchimp.
For high data integrity, especially concerning unsubscribes, latency is a killer.
The superior, more reliable solution is to build a server-side synchronization service using the HubSpot API and the Mailchimp API.
The advantage here lies in Mailchimp’s webhooks.
Instead of your integration tool asking Mailchimp for updates every hour (polling), the Mailchimp API allows you to configure a webhook that instantly notifies a custom endpoint whenever a key event occurs, such as a subscription to a group, an unsubscription from a group, or a general unsubscribe.
Your custom endpoint, hosted on a service like Stape or Google Cloud Platform and configured via a pipeline initiated by Google Tag Manager, immediately receives this notification.
Upon receiving the webhook, the server-side code uses the HubSpot API to locate the contact and instantly set the relevant custom property value (e.g., changing “Red Mail Status” from “False” to “True,” or removing the group membership entirely upon unsubscribe).
This is a better solution because it guarantees near-instantaneous, event-driven synchronization, eliminating the risk of a sales rep in HubSpot seeing a lead as being in the “Red Mail” group moments after they’ve unsubscribed, which preserves data quality and prevents embarrassing or non-compliant communication.
This level of direct API control is essential for accurately maintaining complex, multiple-group memberships and ensuring a true, real-time reflection of your segmentation in HubSpot.
This comment was generated with the assistance of an AI tool, incorporating my expertise in integrations 