Now, if you have a film that is shot at 60 frames per second, progressive. Than that should NEVER be interlaced because you would lose film data.
No film is ever shot at 60 Frames per second - and most likely never will be. There is no benefit for more than 2x cost and this is a significant cost.
As well, if you have a display that can properly show a 24hz source at 24hz (frames per second) then you probably shouldn't interlace that either. But, even if it was interlaced, as long as proper deinterlacing takes place, the original 24fps with full resolution should be able to be restored.
Really, with film there is NO DIFFERENCE, as it is simply how you are transmitting the signal. All the data is the same - PERIOD.
The hard part, is that properly identifying interlaced vs. progressive frame sequences can be difficult for some displays to do on their own, so it is typically better for the processing to be handled by the disc player.
Actually, it is extremely easy for the display to know if it is receiving an interlaced or progressive SIGNAL. The problem occurs with bad deinterlacing in a player outputting a progressive SIGNAL - thus turning off any processing in the display. If this is done improperly to an INTERLACED VIDEO signal, then there could be problems. If the source is FILM and either the source or display can not put this back together properly - then you have a BROKEN device.