From the 2019 Manual
Drive mode cannot be switched in the following conditions:
-ABS/TCS/DSC is operating
-The Mazda Radar Cruise Control with Stop & Go function (MRCC with Stop & Go function) System/Mazda Radar Cruise Control (MRCC) system/cruise control is operating.
-Steering wheel is being operated abruptly
NOTE
If the drive selection cannot be switched to sport mode, the select mode indication flashes to notify the driver.
Not sure how much of this applies to 2016, but I imagine there are similar restrictions.