Non-attachment yes, but total renunciation within the setting of family people is not possible because you cannot build a nice and healthy society with only renunciates. In the world but not of the world, spiritualizing our deeds and thoughts and limiting our dependence on material goods is a good alternative to total renunciation of everything worldly. Celibate nons and nuns however can go some steps further without withdrawing themselves wholy from society.
renunciation of the physical doesn't mean a renunciation of the mental. it would be more along the line of renunciation the ego, or me/mine. like jesus said he who loves his father, mother, son, daughter, or tribalism, is not worthy of me. unconditional love doesn't show partiality based on physical association/connection or characteristics.
attachments, or conditions, are usually made with some thing vs some other. the non-attachment, renunciation would not be conditioned towards anything but unconditional to everything.
unconditional love and infinite intelligence is not associated with an exclusive form