Do you want the application “postgres” to accept incoming network connections?

As you have already discovered, the PostreSQL database server was in fact installed by Resolve. From what I have read, Resolve installs both the CUDA package, as well as the PostgreSQL server. While Apple has had Postgres installed on some previous versions of macOS, I see no indication that it is installed with Mojave, but I could be wrong. There are other software companies which will install Postgres if their app requires it, as you have seen with Resolve.

When you state that you installed a macOS update, are you saying that you installed an update to your current operating system, or are you saying that you installed an update of Resolve for macOS?

In either event, it appears that you only have a few choices, depending on how much you need to use Resolve:

1. You can disable your firewall on the "Firewall" tab in the "Security & Privacy" preferences pane in the "System Preferences" app.
2. You can select the option "Block Incoming Connections" in your firewall settings for that app. I would think that choosing this option should block the connection requests permanently, but who knows.

If the above info has been helpful, or has resolved your issue, please let me know. Thanks! :)