I'm pretty sure the answer to this will be more than obvious, but I've been wondering about the following. Isospin invariance is assumed to be an (approximate) symmetry of the strong interactions. Ratios of cross sections for strong interactions are then given by the appropriate SU(2) Clebsch-Gordan coefficients. These coefficients depend on the third component of isospin of the particles involved; hence the probabilities and cross sections for strong interactions do too. But if isospin is a symmetry of the strong interactions (and let's assume for simplicity it is an exact symmetry), why should probabilities of strong processes depend on the third component of isospin? Since isospin symmetry means (roughly!) that the strong interaction doesn't 'see' any differences between the members of an isospin multiplet, why should the probabilities of strong processes vary depending on which members of a given multiplet are involved?