We have a cape house that is dark red brick on the bottom and white siding on the top. We are putting up black shutters. But what color would be good for the front door?
I'd stick with either black to match the trim or red to match the brick. If you are already planning to add black shutters to a house that is a mixture of red brick and white siding, adding a third color may look a little strange.
You want a door that is going to bring out the best features of your house. It is hard to imagine your house without physically looking a it, but it appears that the black shutters are the smallest aspect as far as curb appeal is concerned. I am not sure why you chose black shutters, seeing as you have red brick, then white siding, so I would make your door black, to help make the house's curb appeal look cohesive. The black door will help tie in your black shudders to the overall appeal, while not making it look like the black shudders were an afterthought.