As a FedEx employee I can tell you FedEx has no such policy. They do constantly monitor and try to optimize routes but more often use more fuel efficient vehicles on longer routes and such.
UPS on the other hand does strive to minimize left turns on their route as stated here.Mythbusters did test this out and determined it was more fuel efficient but took longer. Theoretically is is also safer as more accidents occur when turning left vs. turning right.Not so long ago, UPS drivers worked off maps, 3-x-5 note cards, and their own memory to figure out the best way to run their routes. That changed in 2005 when UPS began to implement a $600 million route optimization system--think MapQuest on steroids--that each evening maps out the next day's schedule for the majority of its 56,000 drivers. So sophisticated is the software that it designs each route to minimize the number of left turns, thus reducing the time and gas that drivers waste idling at stoplights.