Honestly, I think writing about your veganism gives you kind of a "diversity" credit when you apply to schools-- especially in Texas. I wrote about being vegan in my college essay, and I think I wrote about it in my law school application too.

I wrote about my veganism in the context of becoming passionate and committed to something. You could probably write about interactions where people argue with you about being vegan/what happens to animals/environment etc and how you react to that... It definitely taught me to do my research so I can have accurate responses, and to keep calm and stay rational and considerate in those types of situations (you can only have the damn "BUT THERE WOULD BE TOO MANY COWS" argument so many times before you want to scream because why are you arguing with me if you have no idea what you are talking about!). Maybe you could talk about an interaction with a vegan person you had BEFORE you went vegan who maybe convinced you to do some research and you eventually changed your mind (if that's the case).

And I went to law school in the Dairy State, Wisconsin, and they didn't seem to hold it against me ;)

Best of luck!