"Galileo was not the first astronomer to question the (i) _____ view of the Earth as being at the center of the universe, but he was the most vocal, so his ideas were (ii) _____ by the Catholic Church."

Let's simplify this:

"Someone was not the first question ___, but he was vocal about it; therefore, his ideas were ___ by an authority.

Notice that "but he was the most vocal" serves as a justification for a negative action by the authority (the Catholic Church). The second blank has to be something negative then.

Starting with the second blank, let's take a look at the options:

D. authorized (kinda positive, +)
E. proscribed
F. legitimized (positive +)

Even though I was not aware of the meaning of the word proscribed, it seemed likely to me that it was the correct choice, for the other two words carried with them similarly positive connotations.

Turning back toward the first blank, the phrasing demonstrates the injustice of the question: you either know these rather esoteric terms, or you hope for a fortunate stroke of serendipity and guess correctly.

The answers are C and E.