im not sure that the white shirt is a no no with an odd jacket is agreed on across the board. maybe i am misremembering.
Its one of Manton's rules.
I wear white dress shirts with sportcoats in the summer, I like the crisp, clean look that it lends to lighter colored sportcoats where I don't think a blue shirt works. Also, with a khaki odd jacket/ suit, I prefer white to blue. There is also nothing wrong with a navy sportcoat/white shirt.