Cornwall Capp has a dislike towards Bianca Monty at the start of the game, but he does not consider her an enemy. Sometimes if Bianca moves in with them, Cornwall's relationship towards her will be reset, which will cause him to lose his dislike for her. This may not happen if Bianca has met Cornwall before she joins the household.
Juliette Capp has a mutual dislike towards Patrizio and Isabella Monty, as well as a dislike for Mercutio Monty. However she does not consider them enemies and vice-versa. Also Mercutio does not dislike Juliette at the start of the game.
Romeo Monty has a mutual dislike towards Consort and Tybalt Capp but he hasn't gone as far as to consider them enemies.
All the Montys that Albany and Cornwall Capp are feuding with, are not feuding back. In fact they do not even know who Albany and Cornwall are. This is probably because Albany and Cornwall are in-laws and thus are overlooked by the Monty family members.
Despite feuding with four members of the Capp family, Bianca doesn't seem to be very keen to keep the feud going, at least in terms of the Maxis storyline.
I've re-read some of Shakespeare's Romeo and Juliet, and if I'm not mistaken, the Sim Romeo doesn't consider any of the Capps his enemies because it matches the case of the Shakespeare Romeo - a Montague/Monty who has no desire to feud with the Capulets/Capps.
An example of what the feud may have been like before Contessa, Cordelia, Caliban, Claudio, Olivia, and Hero died:
I decided not to portray Contessa Capp and Bianca Monty seeing one another as enemies. It's unknown whether or not this means they were meant to be enemies - but Bianca has a memory of Contessa's death and its the memory for loved ones, not acquaintances. Otherwise I would have estimated them as enemies while they couldn't possibly be friends.