How do I turn off the notification sound for when apps request the current location
Go to Settings > Sounds and Notifications > Advanced > Notifications.

Click on the three dots up in the right corner and tap Show System.

Scroll down to System UI.

Under Categories, tap on VZW, then tap on Importance, select Medium: No sound.



Why is the GPS location notification in the VZW category of notifications? I don't understand. 

I debugged by setting the category sounds to one other than the default, and when going into an app that requested the GPS location, I heard that unique sound, and that let me pin it down to the VZW category.

I do not know what other notifications fall into the VZW category, but they won't be making a sound when the notification shows anymore.