Why does Garmin Golf continue to run in the background on my phone hogging data and battery, even after I close out/sign out and even toggle "force stop"?

Try asking on the Garmin Golf forum. This one if for Garmin Connect.

However if you want to stop any Android app completely (including all background services), and do not mind the lost functionality, enable Developer options (go to Settings » About Phone then tap the Build Number section repeatedly until you see the ‘You are now a Developer!’ message appear), then go to Developer options » Running services » Garmin Golf (or whatever else), and stop all services it uses.