For those people, rear-facing seats can exacerbate motion sickness. See e.g. https://www.sciencedirect.com/science/article/abs/pii/S00036...
I am curious: Unsafe because a " 1970 Plymouth Satellite" or because "rear-facing seat"?
https://www.automobile-catalog.com/img/pictonorzw/plymouth/1...
Looking at that picture, I see belts, but I do not recall those belts and suspect they were deeply wedged into the seat and forgotten about.