This depends a bit on the actual dinnerware.
I suppose crazing can be done to make a special finish and then
covered with another see through finish.
In this case, the crazing is only for decorative purposes and is
perfectly safe.
Crazing otherwise in dinnerware that is not supposed to have
them is another story.
These micro-fractures are not possible to properly clean out and
can contain bacteria and fungus. With time and not high heat and
disinfectant soap, this can potentially be a health risk.
I would not worry too much about it as I always use very hot
water or even a dishwasher at high temperature when cleaning my
dinnerware.