I'm vegetarian. My best friend is INTJ and also vegetarian. I've never thought about type-approach to vegetarianism before, but it's an interesting question.
I would ask what is involved in vegetarianism. Here's what I think, as a vegetarian:
* animal welfare
* environmental preservation and sustainability
* morality/ethics of taking a life when it's not strictly necessary
* personal health
I know that my INTJ and I approach vegetarianism from very different places. So I'm going to write about why I'm a vegetarian and how that reason has changed over time, and maybe that will help some intuitive person identify which elements of vegetarianism have affinities with which personality types.
When I started as a vegetarian, I did a 3-days-a-week thing where I simply limited my meat intake. One one level, this had to do with personal health. I'm from the USA, and the American diet favors meat to the extent that many families eat meat for every meal. A balanced diet, even for meat-eaters, is supposed to be 1-2 servings per day. Since portions in the USA are very large, limiting meat intake to a few times per week was helping me focus on eating more fruits and vegetables and having a healthier, more balanced diet.
Then I met my INTJ. He taught me about the environmental aspect of vegetarianism. He had tons of statistics to the tune of how the amount of corn used to feed cows for a few people in the USA could feed an entire country in Africa and stuff like that, so that being vegetarian isn't just about saving poultry; it's about ending world hunger. When I brought up that the increased demand for soy has people in Brazil slashing and burning the rainforest to plant more crops, he said, "so buy local." So I do, and I'm lucky that I have that option.
With his help, I learned more and more types of foods to eat that did not involve meat. I actually started to eat a much more varied and interesting diet than when I was a meat-eater. At some point I realized that I had only been eating meat once per month. It got to a point where I would eat a hamburger at a restaurant and think, "this vegetarian dish from this other restaurant tastes much better than this." I started thinking about how if I was going to kill something just to eat its flesh, then it better be damn delicious. It was depressing to think that I killed something just to have a not-even-that-good hamburger, especially when navrattan korma or peanut curry taste so much better. I gave myself a rule: I would only eat meat that was raised in a way that would not gross me out or depress me if I saw it before it was processed (legs and beat cut off to fatten in a tiny cage; ears and tails chewed off by other pigs; nothing you haven't heard before). I still believed that eating meat was a natural and normal part of the food chain.
I still do believe that. But one day I was on a picturesque farm in Maine, and they had lambs running around and playing and eating grass on large, open fields. It was absolutely idyllic. The farmers said, "Yesterday we slaughtered a lamb. Today we are eating lamb burgers." I thought: awesome. I ate the lamb burger. It was fresh. It was delicious. It could not have been raised better.
I still prefer navrattan korma. And so I realized that just because I can eat meat, and even if it is natural, I also don't have to eat meat. I am privileged enough to have that choice. So I bucked up and made it. I know that not everyone responds to a vegetarian diet in the same way, or they have food allergies that make it nigh impossible (gluten and soy and nut allergies? OK, I understand!).
In the end, what I'm trying to say is:
* everyone has a different reason for being vegetarian
* those reasons can be based on Thinking or Feeling, and when it comes to health, even Sensing
In the end, I think that people who are vegetarian are simply people who like to think about HOW and WHY and who CARE about things or people or policy-- for one reason or another.
For those of you who are scared of being attacked by paint or chewed out by vegetarians/vegans, I humbly ask you to acknowledge that there are extremists on both sides of the divide, and that frequently the most vocal and aggressive of a group do not accurately represent all members of that group. For example, most vegetarians and vegans I know --and I know a lot!-- do not think positively of PETA.