While the table service restaurants at WDW suggest a dress code, it is not a requirement.
We have gone in everything from park attire to going back to the room and putting on resort casual wear. It all just depends on what we are doing that day, what we are celebrating, etc.
Let me tell you two experiences, and why I no longer overpack..and we are only three hours away.
One night we were heading back to the boardwalk resort from EPCOT. We decided dinner at Flying Fish would be great. We were standing right outside the restaurant in short/tees/sneakers. We called disney dining line..said we need a reservation. No problem, there was availability. The castmember started the dress code speech....I said..oh, then cancel it..we just came from parks and do not want to change. She said..oh no, please..keep the reservation...going in park attire is no problem as long as we weren't in swimwear. I said great. We had a wonderful meal with great service.
Another night..we were at Artist Point. I was in line to check in for our reservation. There was a couple ahead of me..said we would like to eat here but we just came from parks..they were in shorts/shirts/sneakers. The hostess said no problem at all, I don't know why they keep telling everyone of a dress code when we don't have one.
Anyway..go enjoy your table service meals, don't over pack!