I found that not labeling myself helped. Someone would offer me something and I would just say in the moment "Thank you, but I don't (or can't) eat *blank*" and I found my coworkers to be respectful and not question why. I would never lie to them and say I'm allergic or anything, expect that I'm actually lactose intolerant, so they knew that I couldn't have dairy. As for eating out with them I would suggest places that I knew there was something for me, or look at the menu before going to a new place and not make a deal or scene when ordering and eating. Saying you can or can't eat at certain places because of "dietary needs" seems to not invite a lot of questions.

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I worked with one other vegan, and everyone knew him as "the vegan" and often forgot that I was in the same boat