Is the Shimano SL-M590 shifter compatible with XTR RD-M900 rear derailleur? Shimano is known for making their high end components incompatible with their lower ranges (e.g. dura-ace 7400). How do they handle this on their mountain bike range? In my case, I'd like to run a RD-M900 or RD-M910 with a pair of SL-M590 shifters in a 9 speed configuration. Will there be any issues?
Your information is a little out of date, but for 9-speed, all road and mountain rear derailleurs and shifters are cross compatible from xtr and da to Alivio and Sora.
Other combinations work to but for the purposes of your question, there are no issues or likely problems from your component selection.