I would actually argue that both Lords Capulet and Montague are more directly responsible for the deaths of their children than either Romeo or Juliet are responsible. It is Lords Capulet and Montague's arrogance, stubbornness, hatred, and anger that is allowing the ancient feud to persist, even causing three civil outbreaks, as Prince Escalus informs us in his first speech,
Three civil brawls, bred of an airy word
By thee, old Capulet, and Montague,
Have thrice disturb'd the quiet of our streets. (I.i.85-87)
The phrase, "an airy word," can be translated to refer to a "trivial," or unimportant comment. In other words, the Prince is telling us that their arrogance and their hatred towards each other incites them to such rages that their fights can even turn into whole city riots, like we see in the opening scene.
Capulet's and Montague's violent emotions not only wreak havoc on the city, their emotions also influence the emotions and choices of other characters, such as Tybalt. Tybalt would be the next person who is most to blame for the deaths of Romeo and Juliet. He has a hotheaded and fiery temper and the family feud serves to fan these flames of his. One instance in which we see Tybalt's fiery temper lead him to make a bad decision takes place in the first scene. When Tybalt sees Benvolio with his sword drawn, Tybalt immediately assumes that Benvolio is fighting the servants and challenges Benvolio himself, when in reality Benviolio is trying to stop the servants from fighting. We see Tybalt make this erroneous assumption in his lines, "What, art thou drawn among these heartless hinds? / Turn thee, Benvolio! look upon thy death" (I.i.61-62). Tybalt's poor decision to fight Benvolio leads to the whole city riot and his further poor decisions lead to several deaths, including Romeo's and Juliet's. While Tybalt's temper and irrational mind are responsible for his actions and the deaths they cause, it is the family feud that is fueling his actions. Hence, again, the family feud led by Lords Capulet and Montague is the most to blame for the deaths of Romeo and Juliet.
I just want to know all of your opinions. :-)