One may be able to conclude that the contrasts are important because they serve to aid Shakespeare in moralizing about his themes.
As you point out, both Romeo and Juliet believe in fate, as best seen in the line "Then I defy you, stars!" (Act 5, Scene 1), but both also act upon free will, making their own choices, which ultimately lead to their demise. Juliet believed that making vows of marriage so soon was "too rash, too unadvised, too sudden; too like the lightning, which doth cease to be" (Act 2, Scene 2), and Friar Laurence echoed her opinion, even counseling that "these violent delights have violent ends and in their triumph die, like fire and powder" (Act 2, Scene 6). Hence, since Romeo and Juliet's decision to marry so suddenly and without any parental consent is morally questioned, one can say that Shakespeare is questioning the belief in being governed by fate and encouraging more wisely and slowly made decisions, thereby contrasting fate with freewill.
The moral behind the contrasting theme of youth vs. age is also seen in Friar Laurence's speeches. When Juliet fakes her death, Friar Laurence blames her parents, arguing that it was too ambitious for them to want her to be married at such a young age, and even stating, "she's not well married that lives married long" (Act 4, Scene 5). In other words, Friar Laurence is saying that Juliet was too young to be married.
Finally, Friar Laurence is the mouth that even voices the moral behind the contrasting theme of slow vs. fast pace. He definitely feels that Romeo and Juliet have made a hasty and rash decision and tries to talk Romeo out of it. We can especially see Friar Laurence's perspective on the wisdom of making decisions slowly when he says to Romeo, "Wisely, and slow. They stumble that run fast" (Act 2, Scene 3).
Hence Shakespeare's use of contrasting themes serves to pinpoint his moral stance on each theme.
One of the great contrasts in the play is Juliet's "Gallop apace" speech(3.2) and the scene that precedes it(3.1). Therefore, citing Capulet's "Verona brags of him / To be a virtuous and well-governed youth"(1.5.67 or so) and the Friar's speech that begins Act 2, scene 3, one might conclude that the author is recommending the customary seven cardinal virtues.