Non-linear detection schemes can substantially improve the achievable throughput and connectivity capabilities of uplink MU-MIMO systems that employ linear detection. However, the complexity requirements of existing non-linear soft detectors that provide substantial gains compared to linear ones are at least an order of magnitude more complex, making their adoption challenging. In particular, joint soft information computation involves solving multiple vector minimization problems, each with a complexity that scales exponentially with the number of users. This work introduces a novel ultra-low-complexity, non-linear detection scheme that performs joint Detection and Approximate Reliability Estimation (DARE). For the first time, DARE can substantially improve the achievable throughput (e.g., 40%) with less than 2x the complexity of linear MMSE, making non-linear processing extremely practical. To enable this, DARE includes a novel procedure to approximate the reliability of the received bits based on the region of the received observable that can efficiently approach the accurately calculated soft detection performance. In addition, we show that DARE can achieve a better throughput than linear detection when using just half the base station antennas, resulting in substantial power savings (e.g., 500 W). Consequently, DARE is a very strong candidate for future power-efficient MU-MIMO developments, even in the case of software-based implementations, as in the case of emerging Open-RAN systems. Furthermore, DARE can achieve the throughput of the state-of-the-art non-linear detectors with complexity requirements that are orders of magnitude lower.