I have a Nexus 6P, and am using Spotify premium. I've looked over every inch of the Settings tab and can't find how to toggle off the "Publish my activity on Spotify tab."
I also use Spotify on my desktop, and I see it toggled on there. I toggle it off, but it keeps toggling itself back on almost immediately and I'm thinking that's most likely because the phone's setting is set to on. However, as I mentioned, there is no toggle in Settings on my mobile version of Spotify to turn off.