While fate is responsible for the fact that both Romeo and Juliet were born into two feuding families, Shakespeare makes it very evident that the events leading up to the tragic deaths are a matter of choice rather than fate.
For starters, Romeo is not only governed by his own choices, he is a very classic tragic hero and fits Aristotle's commonly accepted definition of a tragic hero by having fatal character flaws. If Romeo had no character flaws that lead to his own demise while otherwise being perfectly virtuous and innocent, the story would be less tragic. Romeo's character flaws are his impetuousness plus his tendency to be guided by his irrational emotions rather than by rational reason, and it is these character flaws that govern his choices in the play. It is through his impetuousness that he allows himself to be persuaded into crashing the Capulet's ball, even though he sensed it would lead to danger. It is through his irrational, emotional drive that he makes the choice to avenge himself on Tybalt for Mercutio's death, even though he knew Tybalt would be killed by the hands of the law. Finally, it is through his irrational emotionalism that he makes the decision to follow through with his own suicide. Shakespeare makes an important issue of the fact that Romeo notices Juliet still looks beautiful in death, that even her cheeks and lips still looked rosy, as we see in Romeo's lines:
Death, that hath suck'd the honey of thy breath,
hath had no power yet upon thy beauty.
Thou art not conquer'd. Beauty's ensign yet
Is crimson in thy lips and in thy cheeks. (V.iii.92-95)
Had Romeo been thinking a bit more rationally at this moment, rather than by being guided by his intense emotionalism, he might have stopped to realize that she really was not dead. The fact that fate misdirected Friar Laurence's letter explaining Juliet's faked death would have been insignificant had Romeo been thinking more rationally; therefore, it is really Romeo's choices, especially his choice to allow himself to be governed by his emotionalism, that leads to the tragedies in the play, especially the final tragedies.
Aside from Romeo, Shakespeare even makes a point that Lords Capulet and Montague have made choices to allow themselves to be governed by their own intense, violent, irrational emotions rather than by reason and that it is these choices that lead to the play's tragedies. We especially see this point made in Prince Escalus's speeches, particularly in the final scene, "See what a scourge is laid upon your hate, / That heaven finds means to kill your joys with love!" (303-04). Notice that he is not saying fate is responsible for Romeo's and Juliet's deaths; instead, he is saying that their hatred is to blame, and Capulet and Montague made the choice to hate and to continue the feud.
Therefore, Shakespeare makes it very evident that, while fate may play a role in certain circumstances, it is ultimately choices that lead to the tragic deaths in the play.