Wideband microwave absorbers, especially those with high optical transparency, are significantly used in civil and military fields. This paper proposes an ultra-wideband optically transparent metamaterial absorber (MMA) with causal optimal thickness and high angular stability. Based on the equivalent circuits model of the MMA, a genetic algorithm is adopted to identify the best circuit parameters that can realize broadband microwave absorption. High transparent indium tin oxide and poly-methyl methacrylate are utilized to realize the absorber. Optimization and simulation results show that the designed MMA presents a high microwave absorption above 90%, covering a wide frequency of 2.05-15.5 GHz with an impressive FBW of 153.3%. The proposed MMA exhibits extraordinary angular stability. For TM polarization, it can still maintain a fractional bandwidth (FBW) over 114.5% at an incidence angle of 70° and over 142% at an incidence angle of 60°, while the FBW of both TE polarization and TM polarization exceeds 150% when the incidence angle is below 45°. Furthermore, the proposed absorber has the advantages of high transparency and polarization insensitiveness. A prototype of the proposed MMA is fabricated and experimentally tested. The measured results are in excellent agreement with the optimized design and the full-wave simulation results, demonstrating its excellent performance. Most significantly, the overall thickness of the absorber is 0.102 λ at the lowest working frequency and only 1.08 times the causality-dictated minimum sample thickness. The MMA proposed herein provides methods to achieve high compatibility with wideband microwave absorption, optical transparency, and wide-angle incidence, thus enabling a wide range of applications in stealth, electromagnetic pollution reduction, and electromagnetic compatible facilities.