As promised, here comes the update now that this issue has been resolved.
In this case, our apps were outright refusing to make the network communication necessary to sign in because of the presence of a self-signed certificate.
This certificate was installed by Kaspersky Internet Security in what I believe to be an attempt to encrypt insecure connections. In this case, from the perspective of our apps, this looked like an attempt to analyze encrypted network traffic to harvest credentials and in order to prevent this from happening, the apps (Both Charts and Navdata Center) disallowed any sensitive requests.
Solution
The solution was quite simple in the end. Just adjust the “Encrypted Connections Scanning” option to match the below and you should be good to go!