Going to be away for 4 months, should we turn off the refrigerator or leave it on with water inside?
If you're gone for a long time, it's good to turn off anything that doesn't really need to be on.  Not only does that not waste power, but it reduces the chance of something bad happening.

The issue with fridges is that they collect moisture inside and they seal well. That's a bad combination if moisture starts out in the box.  The way to deal with that is to address the two issues.  After the fridge has been off for a while, make sure there isn't a pool of water in a tray or someplace.  This includes the result of ice melting inside the freezer.  Once everything is dry, address the second issue by propping the doors open.  The fridge will be no different than any other box then.  There is no reason for new moisture to collect, and it's ventilated anyway.