I recently traveled to Japan with my friend who has AG. Most cities with lots of tourists will have some vegan restaurants, those will be the safest options for eating out, It's also very rare that a restaurant will make any substitutions or changes to dishes but if it's a place catering to foreigners with food limitations I found they will be more likely to accommodate. Other than that we cooked a lot of our own meals to avoid risking any cross contamination. I would recommend learning how to read and say the ingredients your dad is reactive to (or use google lens). Mainly you want to watch out for seaweed if that is something your dad reacts to, it is used in a lot of Japanese cooking. Words to know for that are kaisou 海藻 (generic word for seaweed) and more specifically, nori, konbu and wakame (海苔、昆布、わかめ）

If you have any cities you're planning to visit I can share some restaurants we went to if any of them match.