Mirror-invariance enables recognition of mirrored objects as identical. During reading acquisition, sighted readers must overcome this innate bias to distinguish between mirror-inverted letters (‘d’ vs. ‘b’). Congenitally blind individuals seem to overcome mirror-invariance for Braille letters, too. Here, we investigated mirror-invariance across modalities and its modulation based on the objects’ familiarity. Congenitally blind and sighted subjects participated in same-different judgment tasks using tactile (blind and blindfolded sighted subjects) and visual (sighted subjects) modalities. Stimuli included pairs of letters (Braille and Latin) and familiar non-linguistic stimuli: geometric figures and everyday objects, presented in identical (‘p’/‘p’), mirror (‘p’/‘q’), and different (‘p’/‘z’) conditions. In the tactile modality, no group differences were found in shape judgment for non-linguistic stimuli. In the orientation-based task, higher expertise for haptic rather than visual geometric figures was observed in the sighted group. Sighted participants exhibit difficulties when judging the shape of Latin letters as identical to those presented in mirror orientation (signature of breaking mirror invariance), in comparison to the blind, who had no difficulties in mirror shape judgment for Braille and non-linguistic stimuli. Results suggest that mirror-invariance is modality-independent.