Hi Rebekah! How exciting that your family will be dining at Cinderella's Royal Table! Many little girls dress up in gowns and tiaras for their meal with the princesses, so if your children enjoy dressing up, they would definitely not feel out of place. However, there are also some children who don't dress up, so if your children prefer not to wear princess gowns, they won't be the only ones.
When my daughter was younger, she loved to dress up like her favorite Disney princesses, so she wore a gown over her shorts and t-shirt when we dined at Cinderella's Royal Table. In fact, she ended up wearing her gown around the park afterwards and loved that the Disney cast members called her "Princess" as she boarded the rides. When my daughter became a little older, she elected not to dress up and felt very comfortable dining in the Castle in her theme park clothes.
If your children enjoy dressing up, I would recommend that they do so -- it really is fun for them to dress like royalty for their meal with Cinderella!
Hope you have a magical meal in the Castle!