The present experimental study investigates the shear stripping breakup of single droplets in subsonic and supersonic gaseous flows. In contrast to most research that places emphasis on the Weber number (We), we focus on the individual effects exerted by flow Mach (M_∞) and Reynolds numbers (Re). Millimeter-sized droplets made of either ethylene glycol or water are exposed to shock-induced flows. Shadowgraph and schlieren images of the breakup process are recorded by an ultra-high-speed camera. The experimental We is constrained at 1100, while M_∞ is varied from 0.3 to 1.19 and Re from 2600 to 24,000. A systematic analysis of the experiment series reveals that the breakup pattern alters with M_∞ although a constant We is maintained. The classical stripping behavior with fine mist shed from the peripheral sheet changes to rupture of multiple bags along the periphery at M_∞ = 0.63, and further to stretching of ligament structures from the leeward surface at M_∞ = 1.19. The corresponding breakup initiation is delayed and the resultant fragments are sized less uniformly and distributed over a narrower spread. In terms of the early-stage deformation, droplets experience less intense flattening and slower sheet growth at higher M_∞. The change of Re introduces additional variations, but only to a minor extent.