Is the Shimano SL-M590 shifter compatible with XTR RD-M900 rear derailleur?

The combination of SL-M590, a 9 speed shifter, and the XTR RD-M900, a rear derailleur marketed as "8 speed," will work just fine with a 9 speed cassette. The reason for this compatability lies with the fact that Shimano rear derailleur's of the 7-8-9 speed mountain groups (& 7,8,9, 10 speed road groups) all share the same CABLE ACTUATION RATIO, namely 1.7 to 1. This means that for every 1 mm of cable pulled by the shifter, a rear derailleur in those speed groups moves the same amount of distance (1.7 mm) irregardless of specific speed group. In other words, the rear derailleur doesn't know or care what "speed" it is marketed as because it will move the same distance that is dictated by the shifter. In this case the M590, 9 speed shifter will pull a set amount of cable to shift the chain over the 9 speed gap in the cassette cogs.

With advent of 10 speed, Dynasys, mountain drivetrains the rear derailleur's actuation ratio was changed. Thus you cannot use a Shimano ten speed mountain derailleur in another "speed" system and expect reliable performance. It's not moving as expected as directed by the shifters cable pull.

One thing to keep in mind is that the M900 derailleur has a max high cog of 12 teeth and a max low of 32 teeth. Many 9 speed cassettes are 11-34. Shimano is fairly conservative with their limit numbers and it's common for shifting to work outside of their parameters, but be aware of the potential conflict though it may not be a factor with the relatively small difference in the max numbers of 8 and 9 speed cassettes.