It would seem that having the app installed at all, even with the firewall disabled, prevents certain NordVPN servers from functioning correctly. Examples of this are servers: Canada #244 and Canada #173.
Uninstalling lets you use either the app to connect to those servers or Windows’ built-in IKVe2 VPN connection. Installing Glasswire while connected boots you off and prevents you from communicating with any servers through the VPN. It would seem that GlassWire Control Service is specifically to blame as a few minutes after it’s stopped, the connection resumes working even if the app is open.
This is kind of an issue since I wanted to use both services together, and the servers I listed happen to be some of the closest to me with the most stable and lowest ping.