I work in healthcare too and have 1-on-1 conversations with 30 people a day. But if I’m sat next to someone, the least I can do is say hi. If I am sat next to someone and I say hi and they look at me and completely ignore me, I would consider that person to be a jerk.
I don’t think most people expect you to have a full conversation with them if you are with your family. But saying “ hi, how are you?” before carrying on with your family is the kind thing to do. Not making another person feel like they are raining on your parade simply for following the cruise rules and sitting at their selected table.
All I’m saying is that if you are sat next to someone, please be kind. I’m sure you understand it’s very uncomfortable to feel unwanted. If you prefer not to sit with anyone, maybe skip communal dining and eat somewhere else on the ship if a private table isn’t available.