What is the difference between rigid and strict

"Strict" in this context is either "strong" or "severe" (as suggested in other answers), and "rigid" is "inflexible", or "without exception", though one can also use "strict" as "inflexible", as in "the rule is strictly enforced, no exceptions are made for any reason".

Consider a parent who requires his eight year old kid to be in bed, lights-out, by 10 pm. In my country (Canada), that would not be at all strict as it's quite late. But if there was a punishment that applied at 10:01, or if no exception was ever made (e.g. for watching a meteor shower or the Northern Lights) that would be rigid, though not strict.

Think in terms of rigid as being stiff and strict as being severe and the correct word should fall into place. Eg. His body went rigid with fear. Strict would not be appropriate. Eg. He was under strict orders to be home early. Rigid would not be appropriate.