I know I'm a little late to this party, but here's my take on it (and I apologize in advance for the novel)...
First off, I want to accurately portray myself... I am not a vegan. I don't claim to be. I also don't have a problem with people who are vegan; I just don't personally believe strongly in certain areas where a vegan might. That being said, I am a strict vegetarian, meaning I don't eat animals or animal by-products, so I often get lumped in with vegans when less-health-concerned individuals talk about me.
Now, since I don't eat animal based food, I often get grief from co-workers and friends/family. However, it's all in good fun and I know them well enough to know that they not only respect my eating lifestyle (anytime we have a work lunch or food brought in, I'm always consulted to make sure there is something I can eat; family and friends do the same), but are also impressed by the transition and commitment I've made to eat the way I do.
But that doesn't stop my dad from sending me pictures of shirts that have illustrated deer pooping on some foliage with a caption that reads "My food poops on your food," nor should it. It's actually a funny shirt, it made me laugh.
I make fun of my friends for things they do that I don't, why should the way I eat be off limits? If someone had true derision for the way I choose to eat, then that's a different story altogether, but if a friend or family member is just poking fun at me, I just poke back. Believe me, everyone has something you can tease them about.
From my personal experience, I've found that people usually won't respect someone’s decisions if they don't respect that person. And if they don't respect that person, there's usually a reason; I know it's a cliché, but it's true, respect is earned not given. If someone doesn't respect a decision you've made, it might be because you've previously conducted yourself in a way that makes it difficult for them to respect your decisions (I don't know you and I'm not saying this is the case with you).
Now, since I'm not a vegan, I don't have to stand up for "everything I believe in" (as you put it) when it comes to the way I eat. It's merely a health decision for me. But there are other things I may or may-not feel strongly about (politics, religion, etc...) and discussing those topics has to be done in a careful and delicate manner. Too many people think that if you're not proclaiming your beliefs from the nearest mountain top, you're being a hypocrite (not saying that you're like that). My beliefs are my beliefs, they don't belong to anyone else, so I am very careful not to proselytize when unsolicited. There is a right time and a right way to share your beliefs, but when you order the garden burger at a restaurant and you ask for no cheese and your co-worker asks why you didn't want the cheese on the burger, that doesn't mean you are obligated to say "because I'm a vegan." You could simply say (and in most cases probably should if you're looking to avoid conflict), "because I don't want to eat it." Both are true, one is easier for "a regular guy" to digest. This is another cliché, but there's a time and place for everything.
Man, I'm tired after this one... going to go take a nap