Small kitchens share everything. A vegetable dish can be perfectly vegan on paper and still be cooked next to fish or meat. Vegetable tempura, croquettes and fried tofu often go in the same oil as fish or meat. Grills and hot plates are shared. Ramen shops can use one pot of water or broth for every bowl. Some vegans are fine with this, some aren't: decide your own line before you ask. In a tiny kitchen the honest answer is often “yes”. That's useful information, not a rejection.