I can be both. But I prefer to be a night person because it's so much quieter during the night! But if the need arises, I would be able to wake up early (as long as I have had enough sleep the night before).
Don't listen to them. They don't understand. As long as you are taking care of your cats in the best way you can, that is all that matters. As for vets, it's best to find someone who will listen to you and give you advice instead of putting you down because of how many cats you are taking care...