Prejudice leads to conflict in many ways. The most basic is the ongoing clash between the Montague and Capulet families. In the chorus we're told the feud has been going on for centuries. Therefore, members of both families are predisposed to think badly of one another.
We see this even in Act I scene I, when Sampson and Gregory clash and Sampson calls Gregory "a dog of the house of Montague". We don't know what started this initial clash, but Sampson says he'll take any man or maid of Montague. That tells us flat out he's biased, and he knows it.
Act III scene I is just as open. The scene opens and Benvolio wants to clear out of the streets because the Capulets are around and "the mad blood stirring." To say before something's even happened that people are mad for a fight tells us that this is bias that's soaked deep into the bones of these people.