Embodiments of a core-protecting fan module are provided, as are embodiments of a turbofan engine containing such a fan module. In an embodiment, the core-protecting fan module contains a nose member, a fan rotor downstream of the nose member, a full span stator downstream of the fan rotor, and a splitter structure downstream of the fan rotor. The fan rotor includes a plurality of fan blades, which extends from a rotor hub and which is angularly spaced about a rotational axis. Certain fundamental angular relationships are observed between the angles formed by rotational axis, the nose member, the fan rotor, and a leading edge of the splitter structure to reduce contaminant ingestion by the core flow path and to promote moisture shedding to reduce susceptibility to icing within the fan module, while further avoiding or minimizing negative impacts to other structural and functional aspects of the turbofan engine.