We are dining at California Grill in early December and will be going into the MK for extra magic hours after dinner.
We are staying at an Epcot area resort so going back to the room to change is not an option. Our attire will be weather dependent but most likely jeans, decent tops and park shoes. We will definitely not be dressed up.
Will we be ok?
All of this is a suggestion - it's just what I and my wife do....
We use disguised Park Attire

. Both of us go do WDW with sets of BLACK jeans, no orange crap. Our shoes are BLACK Postal Service sneakers from "New Balance". Mix of long, and short sleeve shirts, with the shorts being Polo's.
In the case of The California Grill - I can walk in with what absolutely look like Black Pants and shoes, and a long sleeve shirt. Same at Shula's. As we depart from dinner, and go to the MK, I can roll up my sleeves, walk into the MK in jeans and sneakers, and be VERY happy.
We also carry a very SMALL, LIGHT backpack - this contains our rain gear, and (in the dead of November) two 300 weight fleece jackets.
Now - V&A? Oh no - suit and tie for me, dress for my wife

. But those same dead-black sneakers work perfectly

.
So - the point about what WE do..... we adjust, generally change for dinner, but we don't let dinner "kill the night"

. Again, just us - we do this for ourselves, and for other patrons - a good many of whom are there at five year intervals, and want to celebrate very SPECIAL events

.