Use the polarizing filter of the monitor itself.
I suggest trying the following with an old laptop or LCD monitor first.
After dismantling, remove the outer layer from the monitor. Now the monitor is completely blank, and whatever is displayed invisible to the naked eye.
Find, make, or buy a frame for glasses, cut the shapes of the glasses out of the removed polarizing sheet, and place them into the frame.
Wearing these glasses - and provided not too many people start doing this - only you can see whatever takes place on your monitor.
Here is a video showing the effect.
See also this answer on Physics.SE.