If Romeo and Juliet had met under different circumstances, their parents might still not have agreed with their chosen mates. However, the consequences would not have been so deadly. It is Romeo’s duel and banishment that causes the real hardship.
If the families were not feuding, the prince would not have declared anyone who duels banished. Romeo would also likely not have dueled with Tybalt, because Tybalt would not have killed Mercutio. Romeo would have no need to flee, and Juliet wouldn’t need to take the poison to fake her death.
You can see how the parents’ feud really does cause Romeo and Juliet a lot of tragic grief. Without it, they still would have had problems, but they would have been typical teenage problems.