To deploy to a website running in Azure App Service using Visual Studio or Octopus Deploy, I have to be able to make outbound connections from my deployment box on port 8172. However this is blocked by my firewall.
Is there any way to change the port used for WebDeploy in App Service?
No, it's not possible to change the web deploy port. This is a configuration of the underlying IIS service which is shared by all users on the same host.