Like the Alaskan brown bear and most other members of the bear family, the diet of the grizzly bear consists of both meat and vegetation.
A) Like the Alaskan brown bear and most other members of the bear family, the diet of the grizzly bear consists -> We are comparing bear and other members of the bear family with the diet. It is incorrect.
B) Like those of the Alaskan brown bear and most other members of the bear family, the diets of a grizzly bear consist -> Diets of bear and most other members are compared with the diets of a grizzly bear. "those of" can be avoided, if we were comparing bear with bear. But, Let's keep it and if we get a better one, we shall drop it.
C) Like the Alaskan brown bear and most other members of the bear family, the grizzly bear has a diet consisting -> This is better than B. Let's drop B and move ahead with C.
D) Just like the diet of the Alaskan brown bear and most other members of the bear family, the diets of the grizzly bear consist -> "the diet..." and "the diets..." are not parallel. Incorrect.
E) Similar to the diets of the Alaskan brown bear and most other members of the bear family, grizzly bears have a diet which consists -> Now, we are comparing "the diets" to "grizzly bears". It doesn't make sense. Incorrect.
So, I think C.