Hi @rowvill,
In addition to the global setting @Richard_Le_ mentioned, you might also consider experimenting (in your preview environment first, I'd suggest) with the three-character status codes behind the Issue and Project statuses (and Tasks, for that matter). Although I've not done so myself for quite some time, as I recall, for the same concept (e.g. "In Progress"), by intentionally changing those codes to NOT match (e.g. "INP" for Project and "YEP" for Issue), you might be able to prevent echoing the Project Status change back to the Issue in such cases (but preserve it, should you wish, in other cases).
Regards,
Doug