What the problem is: You can NOT include the word 'vegan' when posting to /r/food, a subreddit which all new users are initially subscribed to.

What does /r/food say?: /r/Food currently says: "We are a general food sub and do not endorse any dietary regiment over another. We do not allow users to promote their dietary lifestyles or anything politically related here. There are other subs for that."

What do petition signers say?: Just as the phrase 'Mexican food' attracts people who like to eat spicy tacos, the word 'vegan' attracts a wide variety of consumers of vegan products, many whom are not dietary activists/advocates. In this demographic are people who may have to adopt a restrictive diet, often a vegan one, as they have food allergies or a preexisting medical condition; other times, people adopt a restrictive diet for religious and/or ethical reasons. So overall, we are NOT asking /r/food to support animal rights legislation and activist vegan propaganda! We just want users to be allowed to use the descriptor word 'vegan' as this word enables users to easily distinguish between posts and would bring a unique variety of posts to the homogeneous 'meat/dairy' posts currently present on /r/food.

Why not you just post to /r/Vegan?: Users shouldn't have to be redirected to another subreddit which is a subset of a larger community and has a smaller demographic with different interests. Suppose I place a dad joke on /r/Jokes. Would it make sense for a mod to redirect my dad joke to /r/dadjokes even though dad jokes are also allowed on /r/Jokes? French food is a subgroup of food. Vegetables are a subgroup of food. Vegan food is a subgroup of food.