For a general quantum field theory, it's true that the notions of relevant, marginal, irrelevant operators are defined in terms of dimensions of operators. In the special case of a supersymmetric theory, it is natural to study the special case of supersymmetric deformations and the familiar criterion in terms of dimensions can often be reformulated.
More precisely, in a unitary 4d N=1 superconformal field theory, there is a general ("BPS-like") bound, bounding below the dimension of an operator by a multiple of its R-charge. Operators inducing supersymmetric deformations are precisely the operators saturating this bound (chiral or antichiral). For such operators, dimension and R-charge determine each other and so the definition of relevant, marginal, irrelevant can be reformulated purely in tems of R-charge.
The condition R=2 is equivalent to the condition of marginality, itself equivalent to the preservation of R-symmetry. Indeed, R-symmetry is only guaranteed to be preserved in the superconformal case. In the non-superconformal case, R-symmetry is in general anomalous.