Do I need to install the grounding clamp on a water softener if both input and output are PEX?
Assuming this is a water softener that uses electricity, I presume that the ground clamp is put on the lines in the even that one of the lines would become energized, so that it would protect you if you touched the device (and also protects the device).

With PEX, such ground clamps would do nothing (as PEX won't energize) but to be 100% sure you should absolutely contact the manufacturer.  Better safe than sorry.

Edit to add: You SHOULD ground the softener itself, if it uses electrical power, although odds are the electrical line hookup will do just that - you just don't need to ground the PEX lines as well.