If you ask other Jivamukti Teachers, they may respond differently. But this is the way I see it according to my understanding of Jivamukti Yoga.
As a graduate of the Jivamukti Teacher Training program, I was taught that three things make a good teacher: lineage, daily practice, and liking people.
Lineage is having your teachers' blessings for you to teach. Your teachers had the blessings of their teachers to teach, so on and so forth. They acknowledge you and you acknowledge them. Jivamukti Yoga co-founders Sharon Gannon and David Life are rights activists, and the Jivamukti lineage is about compassion for all beings, including (and perhaps especially) animals. Honoring this lineage means that I carry out their teachings in thoughts, words, and actions through living and teaching veganism. Honoring this lineage means that I do not betray the trust of my teachers by explicitly altering their teachings according to my convenience or self-interest. They gave their blessings based on this trust, and I do my part in this teacher-student relationship by being worthy of this trust.
Daily practice refers to devoting oneself to the physical practice of yoga, the practice of oneness and interconnection with all beings. It requires that we connect inwards as well as outwards. By connecting inwards, it means we are constantly challenging our standards of compassion, constantly checking if we can further expand our circle of concern. By connecting outwards, it means we look into other beings as part of who we are, seeing them as similar to us and as having the same right to freedom and happiness as us. Yoga is a physical practice. On the mat, we come into stretches, bends, twists, inversions, balances. Off the mat, we choose what (and hopefully not whom) we put inside our bodies, what we use to shield our bodies with, and how we deal with the physical connection with all other beings. We all share the same space on Earth, and in this sense, we are all literally and physically connected. The daily practice then necessarily translates to the physical actions we take in our daily lives, not limited only to asana but includes our choices for food, clothing, means to earn our living etc.
Liking people in my interpretation means respecting the personhood or individual interests of each being. We may have come to refer to only human beings as persons, but animals are persons too in that they have inidividual interests to be happy and free. To like them is to respect them is to make our intentions not to harm them. Eating animals, wearing them, or using them in any other way harms them, and we cannot like them and intentionally harm them at the same time.
We hear it being said all the time that yoga is a practice, not perfection. That is not an excuse not to do everything that we can. On the contrary, practice emphasizes that we look into what it is that we resist and we dig deep into the root causes of why we resist it.
Veganism is an intention rather than a standard for perfection. A yogi does not have to be a vegan to take Jivamukti Teacher Training, but during the course of the training, immense amount of information about animal cruelty will be presented. He or she can no longer use ignorance as an excuse not to go vegan. The yogi who has the good karma to take Jivamukti Teacher Training has the resources, means, and time to make the transition to veganism. Also, since we are in the practice to heal disconnection, making vegan choices seems to me to be the simplest and most minimal baseline in reinstating connections.
I can understand if my lengthy answer is taken as militant or unforgiving, though that is not my intention. I simply believe that individuals who are drawn to Jivamukti are drawn to it for the same reasons that I am drawn to it. The practice uplifts, empowers, inspires, challenges, teaches, and reminds us that we are whole and holy. It is because of this that we must believe, especially if we want to become Jivamukti Teachers, that our hearts can be so open that there is no need to be stingy with our compassion and no need to undermine our own potential for kindness.
Going back to the question: Do I have to be a vegan to become a Jivamukti Yoga Teacher? My answer is: If you are even slightly considering becoming a Jivamukti Yoga teacher, I think it is because your consciousness is going through a deep process, an emotional and spiritual surgery, if you will. You are attracted to the possibility of ending not only your own suffering but the suffering of others. So be brave, take the Jivamukti Teacher Training, and go vegan. Do it in any order that suits you, whichever comes first, but do it. Believe in yourself. You have it in you.