Rajasthan village crafts, as with other cultures, have developed through the principle that form follows function and incorporate readily available materials fashioned using traditional skills.
A. as with : Incorrect. crafts are wrongly compared to other cultures. the comparison is between rajasthan crafts and crafts of other cultures.
B. as did those of : Incorrect. 'did' displays a wrong meaning. had it been 'as have those of other cultures', this option would have been okay.
C. as they have in : Incorrect. 'they' don't introduce a new entity. 'that' and 'those' do.
D. like in : Incorrect. 'like' is a preposition and a preposition cannot be followed by a preposition phrase.
E. like those of : Correct. The comparison is correct here.