If you decide not to install shelves inside your kitchen sink cabinet, you may need to fit a door stop in the center of the cabinet between the sink support shelf and the cabinet base. This will prevent the doors from swinging into the cabinet and will also add a bit of structural support to the sink shelf. It will also serve to help reduce any visible gap between the two opening doors.
I used a piece of coffee stir stick to make the door stop for my cabinet, gluing it just behind the closed doors so that it stops both doors in the same place. (See photo.)