In some games, you can easily get by without eating animals or without wearing animal products. In
Darkstone for example, you can buy 8 types of food of which 4 are vegan: apples, mushrooms, cherries and grapes. (see attached screenshot)
I'm finding it rather funny to find fresh cherries lying around on the floor of the deepest dungeons but hey, whatever works. Pork chop is the most efficient food in-game as it gives the food meter the biggest boost, it takes up only one square in the inventory and feeds you for 99 points (the max) while an apple or cherries feed you a lot less and take up the same space.
But it's entirely possible to beat the game without eating any meat, fish, chicken or eggs. As for armor, well that would be a bit more difficult. Most RPGs rely on you wearing leather armor at a point, depending on the character class etc so if you're full vegan, that would be a tricky issue.
A fun story about in-game food:
I only played a MMORPG once for a couple days (some crappy free to play Korean browser game) and on one occasion, I teamed up with a guy from Indonesia to power-level in an area with high level monsters. We were getting seriously injured all the time and had to take many food brakes to heal up our characters. I offered him pork from my inventory but he refused, saying that since he was a Muslim he couldn't eat pork even if it's in a game so he used bread instead. That was quite interesting, in fact that was the most memorable moment I had of this game. Because it was something that never happens when you play a singleplayer RPG by yourself, usually you can stuff your characters with whatever you like and they never complain but a real human player reacts completely different, especially if they live on the other side of the planet and have a different religion/culture.