I, too, am confused, but since it was posted under Romeo and Juliet, I will answer it like this. One on one, Romeo and Tybalt would probably have been able to remain civil. Romeo’s shock at Tybalt’s death would seem to support this. When they were by their friends, however, it became a different story. They had their manhood to defend. It would be unseemly to let such an opportunity pass them by in front of their friends. This led to the "tribal crisis".
I, too, am confused...especially with this listed under the Rome and Juliet group. I am assuming you mean that through crisis the community can come together, and in this play, they do. Unfortunately, they wait until both Romeo and Juliet (among others--Mercutio, Paris, Tybalt) are dead before they make peace within the community. This is true for the community of New York and the world with the 911 terrorist attacks, and you can see it plainly again today with the crisis in Haiti.
It would help us a lot to know what you mean by "tribal crisis." I am assuming that it has to do with interpreting the play as a tribal tale. The Capulets and Montagues can be seen as two rival tribes. The love affair between Romeo and Juliet creates tribal crisis not only for the two lovers, who must choose between family (tribal) loyalty and each other, but for the two families, who would have had to address the situation (crisis) if confronted with it. Sadly, the suicides occur before either family has the opportunity to deal with the crisis.
I saw when you posted this as a question. I'm wondering if you can give us any background on what you are talking about. For example, what class is this for? And what do you think "tribal crisis" means? Maybe if we know this we can have a chance to give you a good answer.