I have dealt with this for a while and just stumbled onto the answer that solved it for me.
We have 4 iPhones, my Xs is the main one with the iCloud family account and controls. My wife has an X with no need for restrictions, my daughter has an Xr with restrictions that have had no issues like this one, and my son has an Xr that does have this problem, where the switch for turning on Content & Privacy Restrictions won't stay on.
Every time I've worked on this, I am working from my phone, where the restrictions should be setup and changed from. Today I decided to sign out of iCloud on my son's phone, the one with the issue, and sign back in. That did no good. From my phone, the switch still wouldn't stay on.
I decided I would at least turn on some restrictions from his phone. I went to Settings > General > Restrictions, but it wasn't there. I remembered that it's probably under Screen Time on his phone now as well, so I went to Settings > Screen Time.
Now, he also has an iPad Mini signed into the same account, but which he never uses, so whenever I go to Screen Time for him on my phone, I have to select his iPhone Xr device to see that data, because that is what he uses these days. I started to wonder if the dual devices had something to do with it. Back on his phone, in Screen Time, I noticed at the bottom of the main screen, a switch for "Share Across Devices", which, when turned on, will combine the screen time reports from both his iPhone and iPad into one total report. I enabled this switch. I DO NOT think this made the difference, but wanted to point it out incase it did affect anything.
On his phone, I chose Content & Privacy Restrictions, figuring I'd just set them up there, and once I chose it, entered my Restrictions password, then flipped the switch to on, and began looking through the settings, I noticed that on my phone, which still had the screen lit up and on the Content & Privacy Restrictions page for his phone, that the switch was on and the settings were updating as I changed them on his phone. I think what had happened, is that I previously had Restrictions setup on his phone, with a passcode, and after the update to iOS12 with the Content & Privacy Restrictions settings across iCloud Family accounts, his phone still respected the Restrictions passcode that had been previously setup. Once I entered that passcode on his phone, it released the control of the Content & Privacy Restrictions to my phone, the master family account phone.
So, that is how I got it working, hopefully that helps some of you.
