According to Dr Stuart McGill, twisting your spine is generally safe without a load, not safe with a load (discussed around 20:00 here). However, things may be different for people with bad backs:
For example, flexion-intolerant backs are very common. Stretches such as pulling the knees to the chest may give the perception of relief (via stimulation of the erector spinae muscle stretch receptors), but this approach only guarantees more pain and stiffness as the underlying tissues sustain more cumulative damage. Eliminating spinal flexion, particularly in the morning when the disks are swollen after bed rest, has proven very effective with this type of client. Realize that the spinal disks can bend only so often before damage ensues. Reserve the bends for essential tasks, such as tying shoes, rather than abdominal training.
McGill believes there is a tradeoff between strength and flexibility in the spine, because stretching works by making the annulus between the discs more gooey, which makes it perform worse under load. If you plan to load the spine and are exercising to build sufficient muscle to lock it in place, you can train oblique strength without twisting by doing asymmetric carries such as farmer's walk.
This stuff is gleaned from here, but I am honestly not that familiar with McGill's work so I may be misrepresenting him.