IMO B,

C, D, E are nonsensical
A is incomplete phrase after comma

meat cannot be treated as part of the list of vegetarian foods so u need to have something other than and ----> with

So eliminate A,B and D

C is not idiomatic

so answer should be E

The list of Vegetarian foods end with the , and meal cakes. That is the last item in the list. What follows after that is an exception to the vegetarian food.

the meaning of the sentence is "their diet was largely vegetarian, and meat was a rarity in their diet".

This can also be phrased as "their diet was largely vegetarian, with meat as a rarity"

IMO E.

A and meat rarely
B and meat was rare
C with meat as rare
D meat a rarity
E with meat as a rarity

IMO Answer: E

meat is different than the veg foods (they were abundant but meat rare) and hence not part of same list.
C & E are left.
C: It changes the meaning of the sentence saying that meat was rare, while the original sentence says that meat (as a part of meal) was rare.
E: addresses these issues.

Vinayak