This message is related to the Family Sharing feature of iOS; Threema does not have any influence on it. However, problems with Family Sharing can usually be solved by offloading and reinstalling the affected app. (Creating a device backup first is recommended, see this FAQ entry.)
Go to iOS Settings > General > iPhone Storage > Threema and choose “Offload App”. When this has completed, start Threema again. The system should automatically reinstall Threema without losing any data.
