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1.
A fundamentalist vegan who goes around proselytizing vegetarians and omnivores.

A vegan intolerant of any other diet, or anyone who adheres to a diet other than a vegan diet.

Dynise Balcavage, a vegan, regarding her omnivore husband: “I’m not a vegangelical,” she said. “He’s an adult and I respect his choices just as he respects mine.”

-"I Love You, but You Love Meat"
New York Times, February 13, 2008
by Yosef G. February 13, 2008
 
2.
A vegan who thinks that any other lifestyle choice besides veganism is wrong; one who similarly pushes veganism on others, often in a proselytizing way.
"I’m not a vegangelical," Dynise said. “John’s an adult and I respect his choices to eat meat, just as he respects mine.”
by johnny haze February 13, 2008
 
3.
Vegetarian or vegan who not only refrains from meat or animal products themselves, but expects others too as well. Somewhat preachy with their views.
I ordered a steak and Stacy just gave me a disgusted look. She's such a vegangelical.
by Square hippie June 01, 2009
 
4.
An annoying , self promoting Vegan.
I was eating a Baconator and she got all Vegangelical on my ass.
by Eddie Classeerole December 07, 2009