http://deansomerset.com/2010/12/21/why-spinal-flexion-isnt-going-to-kill-you/
It's probable that the greatest risk from weighted ab work is not the effect the movement itself has on the spinal discs, but that the strengthening of the iliopsoas that comes with most core flexion work contributes to lumbar lordosis/anterior pelvic tilt, which most people don't need any more of; walking around in lumbar hyperlordosis greatly increases your rate of disc damage.
You have to take the same holistic view when assessing the pros and cons of neck work: if you're in cervical hyperlordosis (i.e.
forward head posture) you shouldn't be doing neck extension work (like bridging) which will make the misalignment worse. Contrariwise, cervical hypolordosis (i.e.
military neck), it's neck flexion work you should be avoiding.
In either misalignment, vertical loading of the neck is going to result in asymmetrical loading of its discs, and eventual herniation.
Keep the c-spine neutral though, and theoretically you should be fine. As Somerset states, spinal flexion is a natural movement and we should be able to load it; only if a movement is exacerbating an existing postural misalignment does it become definitely inappropriate.