Surely both have to be set up for PS ; otherwise the receiving device (projector in your case) would be expecting the wrong format/scan rates etc.
Only exception would be if the projector had some form of autodetection of the applied input mode.
Not being overly conversent with projectors, I am not sure whether or not this is common.
well in my case i can decide on the projector if the de-interlacing is made on the player or on the projector.
so i can set the dvd player to interlaced and the projector does the de-interlacing.
and if i set the dvd player to progressive the projector just projects the image as received...
Only one must be set to progressive, so to use the DVD players de-interlacer set this to progressive and turn off the PJ's built in de-interlacer or the other way round would be to set the DVD player to interlaced output and then allow the PJ to de-interlace.
Sometimes having both set to progressive can cause problems as the PJ will be trying to de-interlace an already progressive signal.