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I suspect part of the confusion is due to the fact that the $SU(2)$ appearing in the Standard Model gauge group $U(1)\times SU(2) \times SU(3)$ is different from the $SU(2)$ of the Cassen-Condon paper. The latter is usually called isospin and is an approximate global symmetry of nuclear interactions. It is only an exact symmetry in the limit that one ignores electromagnetic interactions and the mass difference between the up and down quarks. The $SU(2)$ of the standard model gauge group on the other hand is a (local) gauge symmetry. I'm assuming here that you understand the difference between global and local symmetries as there phrases are used in the physics literature. If not, please consult any book on quantum field theory.