As has been stated already, there are two types of rivalries: malignant rivalries, and playful rivalries.
Luckily, I know of only one or two malignant ones in FIRST. These should definitely be discouraged, as nothing good can come of them. Why spend time despising each other, when you could instead be helping each other out? Gracious Professionalism - take it to heart, make it your mantra. It goes right there with the big mottos like C'est la Vie, Carpe Diem, Hakuna Matata, etc.
As for playful rivalries, I think they maybe should even be
encouraged. As Joe Brown said, "
A challenge is an opportunity to prove your ability to yourself, and others." Take for example 118 and 148, which has already been talked about. They are two of the best teams in Texas, and both graciously and professionally 'nudge' each other, making one another strive for more. They are making each other grow, and causing each to try more to be the best they can be. In my eyes, 148's
Operation Playhouse was genius. As long as both teams know that it's all in good fun and help each other out, I don't see any bad side to it. In our team's own experience, a few of our more experienced members and those on Team 25 commonly 'nudge' each other, making each of us try harder to excel. No hard feelings come of it, and we each make one another come a better team. For example, last year, Shaun, the drive coach of 25, made a bet with us saying that if they won World Championships, he would finally let us reveal the contents of his backpack. And, wah-lah, they won Champs for the second time in 12 years. If that's not excelling, I don't know what is. (Our next bet is that if we make it to Einstein this year, he will
give us his backpack, and he will get a new, see-through one to wear

).
Anyway, my point is: if it's G.P., it's O.K.