This paper derives an achievable rate-distortion (R-D) region for the state-dependent discrete memoryless multiple access channel (SD-DMMAC), where the generalized feedback and causal side information are present at encoders, and the decoder performs the joint task of message decoding and state estimation. The Markov coding and backward-forward two-stage decoding schemes are adopted in the proof. This scenario is shown to be capable of modeling various integrated sensing and communication (ISAC) applications, including the monostatic-uplink system and multi-modal sensor networks, which are then studied as examples.