SOOKIE: I’ll make cookies [to celebrate Rory getting into Chilton]. Protestants love oatmeal.
Sookie has a number of eccentric beliefs in regard to food, and this seems to be one of them. The reason for her statement is something of a mystery to me, unless she is thinking of Quaker Oats, whose logo has a man dressed in 18th century Quaker clothing to represent simplicity and honesty. (The company was not founded by Quakers, and never had any connection with the religion).
The interesting part is that her saying this seems to imply that Sookie herself is not a Protestant, although this is never confirmed in the show.
The Annotated Gilmore Girls 