how do you know someone’s vegan? they’ll tell you

That statement reads to me the same as “how do you know someone has food allergies? They’ll tell you.”

EDIT: Just to be clear, I know that allergies are different than boycotts. If the girl could get anaphylactic shock from a drop of milk, the dad would be justified in reacting that way. However, in both cases, it makes sense to inform people that you can’t/won’t eat something.