The sensitivity of the stability of the ideal n = 1 internal kink mode to variations in the plasma profiles is analysed both analytically and numerically in rotating tokamak plasmas. These stability analyses have been carried out including the centrifugal effects of toroidal plasma rotation upon the equilibrium, and also inconsistently when the equilibrium is treated as static. The change in plasma stability due to rotation is partially (consistent equilibrium) or wholly (inconsistent treatment) determined by the radial profiles of the plasma density and rotation velocity. It is found that the internal kink mode stability is strongly influenced by small variations in these plasma profiles. The implications of this extreme sensitivity are discussed, with particular reference to experimental data from MAST.