How can I move from iOS 11 Developer to iOS 11 Public
Remove any profiles that are in the settings app (general section)  relating to the developer program. 
Enroll the device in the public beta program with a public beta profile. 
Wait for the public beta build to be a newer version than your current Dev beta and then update the device. 


If the Dev beta is too new or you never get an available update, you might need to erase and restore / recover the device. Since you ask this early in the 10.11 beta cycle updates should be every couple of weeks for a while. This shift isn’t a given and could break in the future even though it worked a few times in the past.