I had a similar problem with a Monoprice HDMI splitter connected to a 2D projector and a 3D projector. I think it's caused by the player detecting the 2D projector even though it is ostensibly turned off.
I use a Harmony remote.
My 2D projector has 2 HDMI inputs. I use only one of them, HDMI-1.
Now when I turn off my 2D projector, I have the Harmony first send a signal to set the input to HDMI-2, the unused input. This solved the problem.
I also set the 2D projector to automatically detect which input is active when it is turned back on. This was easier and worked better than having the remote send a HDMI-1 signal.