I used to cruise Disney a fair amount. Dining times are set, but seating is more flexible than some folks realize. On some cruises, with our family of 4, we were seated with another family of 3-4, with kids about the same age as ours. My husband and son are very social, and they enjoyed the interactions. My daughter and myself (both introverts) didn't chat a lot, and that was fine. Other times, we requested a four-top, which was granted. When just daughter and I cruised, we requested a table for 2, and that was granted. When I sailed solo, I requested to dine alone, and that was granted. While dining seating requests (made prior to sailing) are not guaranteed, I never had one denied.
I loved the service and the ships with Disney. Not the itineraries nor the cost. Thus our move to NCL.