It is very common question among the society even we all are agree that the uses of clay kitchenware is best for health.
The reason is that we are not used to with these kitchenware.
And the process of cleaning these is similar to washing of other utensils, only care following

1.  Should wash immediately as soon as possible

2.  Should uses herbal/organic based dish wash or liquid.

3.  Should use separate scrubber.

4.  Keep dry the utensils for long life.