OK, the plot thickens here...
I ordered TWO HP Envy displays to go with my new Mac Mini, but the behavior I have described up until now was for just one of the monitors -- using an HDMI connection.
Today the Mini DisplayPort to DisplayPort cable I ordered online for the second monitor arrived. When I replaced the HDMI cable with the DisplayPort cable two things happened:
1. I was able to turn Night Shade on and off; and
2. The effect of Night Shade is now much more subtle. Whereas I was getting strange purple and orange and pink colors with the HDMI cable I actually enjoy what Night Shade does when using the DisplayPort cable.
So now I am a happy customer. I've just ordered another one of the DisplayPort cables and I think I'll be fine.
One thing I will say, sarah_s1, if you work for Apple: In order to use Nightshade from Sunset to Sunrise I had to give the system permission to know my location (so as to set the time zone). In my case I had to restart my machine to get that permission to take effect. If that is normal operation I suggest you notify the user that a system restart is required.