As I understand, one probably will not find Red Meats, Chicken, etc. at a Orthodox monastery. One will definately find Wine, oil, and fish when it is permitted (non-fasting days).
However, remember that non-vertebrate are allowed during most fasting times (calamari, shrimp and other).
It is correct that some monastics are complete vegetarians (and some probably vegan).
Ironicially, if one follows the strictest rules of fasting, we are even more vegan than vegans sometimes during the fast. No oil (no frying). Dry eating is super vegan, lol.