Is it safe to use dinnerware with crazing?

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.