For a set of positive integers A ⊆ [n], an r-coloring of A is rainbow sum-free if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow Erdős-Rothchild problem in the context of sum-free sets, which asks for the subsets of [n] with the maximum number of rainbow sum-free r-colorings. We show that for r = 3, the interval [n] is optimal, while for r ≥ 8, the set [⌊n/2⌋, n] is optimal. We also prove a stability theorem for r ≥ 4. The proofs rely on the hypergraph container method, and some ad-hoc stability analysis.