This paper focuses on molecular communication (MC) systems where the signaling molecules may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can realize the concept of constructive and destructive signal superposition, which leads to favorable properties such as inter-symbol interference (ISI) reduction and avoiding environmental contamination due to continuous release of molecules into the channel. This work first derives the maximum likelihood (ML) detector for a binary MC system with reactive signaling molecules under the assumption that the detector has perfect knowledge of the ISI. The performance of this genie-aided ML detector yields an upper bound on the performance of any practical detector. In addition, two suboptimal detectors of different complexity are proposed. The proposed ML detector as well as one of the suboptimal detectors require the channel response (CR) of the considered MC system. Moreover, the CR is needed for the performance evaluation of all proposed detectors. However, analyzing MC with reactive signaling is challenging since the underlying partial differential equations that describe the reaction-diffusion mechanism are coupled and non-linear. Therefore, an algorithm is developed in this paper for efficient computation of the CR to any arbitrary transmit symbol sequence. The accuracy of this algorithm is validated via particle-based simulation. Simulation results using the developed CR algorithm show that the performance of the proposed suboptimal detectors can approach that of the genie-aided ML detector. Moreover, these results show that MC systems with reactive signaling have superior performance relative to those with non-reactive signaling due to the reduction of ISI enabled by the chemical reactions.