We perform low-temperature magneto-conductance measurements on Cu and Au thin films with adsorbed chiral molecules and investigate their phase-coherent transport properties. Upon adsorption of chiral molecules, the spin-orbit coupling strength in Cu decreases and the Au films become ferromagnetic as evident from weak localization and antilocalization data. A theoretical model indicates that anisotropy in the molecular tilt angles, provided that the chiral molecules act as magnetic moments, induces a nonvanishing magnetic exchange interaction, causing changes in the spin-orbit coupling strength in Cu and Au. Our work adds a new viewpoint to the plethora of unique phenomena emerging from chiral molecule adsorption on materials.