Disc brake pad and rotor compatibility The SM-RT53 rotor should be used together with resin pads. If it is
  used with metal pads, the pads will wear out very rapidly.


from Shimano BR M-416 disc brake manual

How do I know if a rotor is compatible with organic pads prior to purchasing? Is it true that all rotors are?

How do I know if a rotor is compatible with sintered pads prior to purchase? Why not every rotor?
I have to say I never consider which pads I'll be using with rotors when I buy either. I buy organic for best stopping power and metallic for longest life (kevlar somewhere in the middle). 

For mountain biking, the weather and type of mud/grit you're riding on is a FAR greater killer of pads than a rotor; you can easily get through a new set of pads in a few hours in sandy and wet conditions.