We demonstrate that crossing symmetry of S-matrices can be violated in theories with non-invertible symmetries. Focusing on integrable flows to gapped phases in two dimensions, we show that S-matrices derived previously from the bootstrap approach are incompatible with non-invertible symmetries along the flow. We present consistent alternatives, which however violate crossing symmetry and obey modified rules dictated by fusion categories. We also show how these modified crossing rules can be used to constrain the space of amplitudes with a given categorical symmetry.