The correct answer is (A).
The phrase the extent to which is idiomatic and introduces a subordinate clause that modifies the extent. The verb has been shifted is in the passive voice, which is appropriate because the light is not the agent of the action, but the object. The other answer choices have various errors:
(B) The verb has shifted is in the active voice, which implies that the light shifted itself, which is illogical.
(C) The word that is not an appropriate subordinator for the extent, which requires to which.
(D) The use of the gerund shifting changes the meaning of the sentence and implies that the light is still shifting.
(E) Answer choice (E) is wrong for two reasons. First, it uses the preposition of instead of to which, which is not idiomatic with the extent. Second, it uses the noun the shift instead of the verb has been shifted, which makes the sentence wordy and awkward. The noun the shift also introduces ambiguity about whether the shift is a single event or a continuous process. The verb has been shifted clearly indicates that the shift is a result of the galaxy’s motion away from the Earth.