Our subject in this sentence, Connor, is described as being so opposed to something that he flushed, meaning his face turned red, and stormed out of a room, meaning he went out in a passionate and angry way. We are looking for a word that describes this passion and anger.
"Tacit" means that something is implied or indicated but not actually expressed in words. If Connor did not verbalize his opposition, it may have been tacit. But tacit does not convey the fuller meaning of a feeling so strong it created this intense behavior of his. "Unconditional" means not limited, complete and absolute regardless of circumstance. This word might apply if Connor is unwilling to change his stance no matter what the circumstances, but again, it doesn't reference the emotion described. "Uninformed" means to be without knowledge on a topic. Nothing about the sentence tells us whether Connor knows about the topic or not. "Abject" means completely without pride or dignity, but our subject is full of spirit.
The word "fervent" fully captures what is happening. "Fervent" means to be marked by a great intensity of feeling. Connor shows by his storming out that he is passionately in opposition to the project. The flushing of his cheeks even implies his face is hot with feeling, perhaps anger, and that heat also matches the word fervent.
The correct answer is (A).