Low-altitude unmanned aerial vehicle (UAV) networks are integral to future 6G integrated sensing and communication (ISAC) systems. However, their deployment is hindered by challenges stemming from high mobility of UAVs, complex propagation environments, and the inherent trade-offs between coexisting sensing and communication functions. This article proposes a novel framework that leverages movable antennas (MAs) and intelligent reflecting surfaces (IRSs) as dual enablers to overcome these limitations. MAs, through active transceiver reconfiguration, and IRSs, via passive channel reconstruction, can work in synergy to significantly enhance system performance. Our analysis first elaborates on the fundamental gains offered by MAs and IRSs, and provides simulation results that validate the immense potential of the MA-IRS-enabled ISAC architecture. Two core UAV deployment scenarios are then investigated: (i) UAVs as ISAC users, where we focus on achieving high-precision tracking and aerial safety, and (ii) UAVs as aerial network nodes, where we address robust design and complex coupled resource optimization. Finally, key technical challenges and research opportunities are identified and analyzed for each scenario, charting a clear course for the future design of advanced low-altitude ISAC networks.