My experience being a vegan and sailing on X, is that wherever I dine, I can construct the menu to my liking and needs/desires.
I Am a low-fat vegan and there has been very few issues IME....
Let X Special Services know before you board and once on board, let the Maître d' know and then your wait staff in the MDR...
You can get the next nights menu in advance and then construct your meal from there... This is not to say that there will not be a foul up here and there, yes, there could be and as such I Am vigilant until I feel comfortable that all is working okay... in the kitchen.
Same for Specialty Dining, they will talk to the MDR kitchen about what to prepare if you do not provide them an idea of what is good...
bon appetit and bon voyage