Imho...
It depends on your definition of 'safe'.
Opening the contactors while moving
will kill the inverter. But could protect the battery from overvoltage/overcurrent/etc. So allowing the BMS to open the contactors will likely kill your inverter in the event of a problem, but may better protect your battery, hopefully avoiding a fire. 'Safe'
On the other hand, leaving contactor control to the inverter controller will protect the inverter, and the inverter controller should respect messages from the BMS, limiting currents and voltages. It would take a remarkable series of malfunctions for the inverter to demand excessive current
and ignore the BMS screaming to slow down! 'Safe'...
Another option would be to let the BMS open contactors, but set it's thresholds quite 'relaxed', and have the inverter try to limit voltages and currents more strictly - the inverter to try to keep the battery and BMS well within its' 'happy' range, but the BMS could still take over and try to protect the battery in the even of a serious problem.
But... considering overall risk... The likelyhood of a battery fire due to transient over-voltage or over-current while driving is actually very low (total energies will be low, and thermal mass is quite high). Excessive temperature is a problem, but much slower, so
assuming good monitoring of the pack should be relatively easy to spot a problem before it becomes an actual issue. Battery safety while
charging is a different issue - the car will be left unattended with current (energy) being fed into it. But the car will be sat still (hopefully!) so the BMS opening the contactors shouldn't upset anything (the charger should happily error out). Again, setting the limits on the charger more conservative than the BMS 'error' conditions should be kinder on the system.
Note, if you've got an induction motor, turning off the inverter (or killing it) while moving is
usually relatively benign - magnetic field disappears, so the motor turns into a lump of spinning iron, and the driver retains control while the vehicle coasts to a halt. With a permanent magnet motor, stopping the inverter can essentially short the three motor phases resulting in very high uncontrollable regen. This could be a problem at speed... 'Safe'?
(I think the SDU is induction, so not a problem in your case) (See below)