Google Smart Lock constantly asking to turn on Bluetooth
I'm having the exact same problem and there are no references to it on the internet except this StackExchange post and a dupe post on another site.  I still don't understand why it's happening or what's causing it.  It doesn't appear to be tied use of any particular app, and sometimes pops up simply when I pick up my phone and unlock it.  

I thought disabling Google Advanced Protection would make this go away.  However, even with it disabled and all hardware tokens removed entirely from my account, I still get the popup on my iPhone saying "Turn On Bluetooth to Allow "Smart Lock" to Connect to Accessories".  I uninstalled the Smart Lock app and I haven't seen it pop up since.  

So - my workaround is basically not using Google Advanced Protection at all.  

I may attempt to re-enable it and do more troubleshooting when I have time.  One thing I forgot to do was go into my iPhone bluetooth settings and "forget" any previous pairings.  Maybe that has something to do with the popup if it's looking for a past device.  Will post edits here if anything changes!