The other day, I was in a company meal with ~20 coworkers and someone offered me wine before adding: "At least you know this is vegan." (because I'm vegan). I don't like alcohol so I politely refused before adding with a smile: "In fact, not all wines are vegan" (which is true). After that, all of my colleagues started to laugh at me like I was some kind of silly person who didn't know what she was talking about. And even after I try explaining myself, they still didn't believe me (because I was unable to give details).
I'm the youngest person at my company, I look very young (I'm 23 but people regularly assume that I'm under 18), I'm a woman, I have been working there for three years and I'm like a student doing an internship (it's an simplification, my actual status is "étudiante en alternance" which mean I spend half my time in school and the other half at work; Kevin mentioned that it's called "co-op" in the U.S., and eggyal added that it's a “placement” in the U.K.).
What I tried
After my colleagues started laughing, I tried to explain to them that it was true and that during the process of fabrication, products of animal origin were used. They started pressing me with questions. Unfortunately, I didn't know much about what animal products were used, when and why (since I don't drink alcohol, I didn't care about the details). So, I tried to answer their questions but told them that I didn't know much about the subject and suggested that they find out on their own (implied: instead of asking me questions I couldn't/was not qualified to answer). My phone can't go on internet and they didn't care to google it up.
Since I'm vegan/vegetarian, I have to deal with this behavior a lot (this is just the most recent example). Normally, saying something like "I read that..." people are fine with, but when it comes to veganism, they aren't anymore. As a result, I try to learn every fact about veganism by heart so that I would be able to defend myself when someone is trying to ridicule my vegan commitment. But I'm only human and this is hard. Plus, turning myself into a human Wikipedia isn't really my dream.
How do I convey to my coworkers that: I don't know the details, they can look it up themselves (so they don't have to blindly trust me) but, please, stop assuming that this cannot be true and that I'm silly/stupid/whatever?
More important, how do I make them stop laughing at me? (I cannot control what they think but it would be nice if they didn't express it that clearly).
Note and clarification
I'm not good at human interaction and the only real social life I have is with my extended family (a big one, but still). Also, I hate conflict so, please, do not answer with a conflict-oriented solution.
There were 20 people there: some with whom I take my coffee breaks and that I like; some with whom I work in my day to day life and with whom I eat everyday; my direct boss (N+1) with whom I really don't get along (he is sexist, among other things); the big boss who likes me but doesn't like my N+1; and others. None of them were vegan/vegetarian.
I responded because they were talking to me and they said something false. I know a lot people think I should not have said anything, but leaving someone with a false belief seemed (and still seems) wrong to me.
Strong emphasis: The argument wasn't about me being vegan/not drinking wine. It was about them note believing my statement ("not all wines are vegan") which I couldn't backup with precise and complete details (just a vague "animal products are used during the manufacturing process"). Details that they asked for. And since I didn't had enough details, they were laughing in disbelief while not carrying enough to fact-check.