The enmity and rivalry between the Capulets and the Montagues propels events forward after it happened by chance that Romeo and his friends were invited, though their identities were unknown, to Capulet's party. It was here that the other critical element catalyzing the rushing of Romeo and Juliet to their deaths is introduced in the person of Paris, with whom Juliet's parents are arranging a marriage on Juliet's behalf.
Had the feud not been raging between Capulet and Montague, perhaps Juliet could have made a successful case to her parents that she be allowed to marry Romeo instead of Paris, whom she thoroughly disliked. It was to escape an impending wedding to Paris that more fuel was added to the catalyst of the feud that was driving Romeo and Juliet forward.
JULIET: I will not marry yet; and, when I do, I swear,
It shall be Romeo, whom you know I hate,
Rather than Paris. These are news indeed!
It was directly related to the feud between the families that Romeo came to slay Tybalt. The youths of each house unfortunately met with unresolved grudges for the death of Mercutio; it was almost inevitable that more tempers would flare causing Romeo to be a murderer and the assassin of his new wife's kinsman.
In a direct connection to the catalyst of the family rivalry, it was this confrontation between the youths of each feuding house that forced Romeo into exile thus forcing Juliet to a desperate plan to escape a polygamous marriage to Paris, thus forcing Romeo to return to try to save her. He returned at the wrong time, arriving too soon so that he sees only the herb induced comma. Had the families obeyed the Prince and sought peace--without the sacrifice of their children first--there may have been no unquenchable catalyst to drive their demises forward.
PRINCE: Where be these enemies? Capulet! Montague!
See, what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love.
And I for winking at your discords too
Have lost a brace of kinsmen: all are punish'd.