We had the same issue in our ClickDimensions implementation. We are sending:
When somebody unsubscribes via ClickDimensions, we were not able to send the transactional emails via ClickDimensions anymore.
This how we worked around this
When somebody unsubscribes, ClickDimensions:
Run when the 'Unsubscribe' record is created
If Unsubscribe:Contact contains data
On record Contact
Set DoNotAllowBulkEmail = false
Set DoNotPromote = true
On record Unsubscribe
Copy the email to a custom field called 'original email' for us to keep the history
Clear the field 'email' and the field 'contact' <-- This has to be done because ClickDimensions will not send emails if those fields contain data OR the contact's DoNotAllowBulkEmail is set to true.
This was done before I joined the company, so I don't know whether it was suggested by ClickDimensions or not.
Hope this helps