Bizarrely, the most plausible race for a vegetarian who protects the fauna of Tamriel might well be the city-dwelling Cyrodiils. According to the first pocket guide,
This describes how the religious principles on respecting nature (dictated by the various naturalistic cults and spirits of the early Cyrodiils) restricted their ability to make use of their own surroundings, and many have interpreted this as meaning the Alessian Nibenese were largely vegetarian. Perhaps your character could be part of a revival of this system, representing a facet of Kynareth that is opposed to the modern views of Imperials or Nords whereby nature is a thing to be exploited? Issues in this might arise if the character in question is not an Imperial by race - the Alessian Order were very Cyrodiil-centric - or if they find they cannot hold true to the more oppressive doctrines espoused by that early religious movement (namely, opposition to anything Elven in origin). However, the days of the early Reman dynasty might have espoused a milder version of this belief, welcoming other races and provinces while maintaining the respect for the earth and beasts of Tamriel - especially since the myth of Reman Cyrodiil 1st describes how he was quite literally born from the earth.