A) but fierce domestic competition -- Incorrect idiom. "Not so much X, as Y" is the correct idiom.
B) but domestically fierce competition -- Same as A. Also "domestically" fierce competition changes the meaning. The noun is "domestic competition" and the adjective is fierce, indicating that the domestic competition is fierce. The usage in this choice is rather awkward. "domestically" is now an adverb modifying the adjective "fierce", which modifies the noun "competition". Changes the meaning.
C) but rather it is fierce domestic competition -- Same as A. Incorrect idiom.
D) as it is fierce domestic competition -- "Not so much X, as Y". Correct idiom. I would argue that "it is" is rather redundant here. The sentence would be clear even without them. Keep.
E) as competition that is fierce domestically -- Changes the meaning. We are not talking of a specific "type" of competition (indicated by relative pronoun "that" and the rest of the clause "is fierce domestically") but we are describing qualities / characteristic of that competition. This one changes meaning. Eliminate.