The shear failure and friction mechanisms of bioinspired adhesives consisting of elastomer arrays of microfibres terminated by mushroom-shaped tips are investigated in contact with a rigid lens. In order to reveal the interplay between the vertical and lateral loading directions, experiments are carried out using a custom friction set-up in which normal stiffness can be made either high or low when compared with the stiffness of the contact between the fibrillar adhesive and the lens. Using in situ contact imaging, the shear failure of the adhesive is found to involve two successive mechanisms: (i) cavitation and peeling at the contact interface between the mushroom-shaped fibre tip endings and the lens; and (ii) side re-adhesion of the fibre's stem to the lens. The extent of these mechanisms and their implications regarding static friction forces is found to depend on the crosstalk between the normal and lateral loading directions that can result in contact instabilities associated with fibre buckling. In addition, the effects of the viscoelastic behaviour of the polyurethane material on the rate dependence of the shear response of the adhesive are accounted for