It may be easier if you use a lower status to opt out of chatting. If you spend time with someone who has never had a chance to discuss their daily routines, it is possible for them to say "I never learned to explain this." It is a simple method of explaining how troubling a conversation is. You can continue to reinforce the argument with statements of support.
- I don't normally talk about it.
- I don't get involved in outreach.
- I couldn't debate this subject if I tried.
- I leave the talking to other people.
- I'm not the best person to talk to.
- Talking about this is annoying and I don't feel good about it.
- I don't know a way to summarize it.
A denial of qualification permits you to work to your strengths in telling people that you don't like being questioned. It's honest, and if they find that tiresome, that's their problem. At some point, you can call out any ongoing harassment. All you have said is that you want to avoid a controversial subject with the person. You have the right to abstain from any subject, and that has nothing to do with veganism. Etiquette requires that they drop it.
This practice also allows you to follow up if you are publicly addressed as "the vegan". You ask people not to identify your veganism because you don't want the subject mentioned simply to avoid discussing it. Again, the etiquette requires them to drop it. It won't stop everyone, but you can certainly tell when people are passive aggressive over the controversy surrounding veganism. If they hate veganism, and become enthusiastic about discussing it, then you have previously earned an opportunity to demand a way out of being their trapped audience.
And best of all, any ongoing discussion of your daily practices can be forced into the simpler category of "monkey see, monkey do". If they have an interest they will follow along with easy discussions about vegan things - not reasons.
One negative of this approach would be dinner conversations. Dinner conversations have the right to be about hobbies and food. It would be bad etiquette not to discuss a little about veganism and vegan food at a dinner party. Perhaps be ready to discuss it, and signpost the points that get into heavy controversy. I'd suggest getting in some practice before attending a holiday dinner with extended family.