Tactile exploration of surfaces is a key component of everyday life, allowing us to make complex inferences about our environments even when vision is occluded. The emergence of biomimetic neuromorphic hardware in recent years has furthered our ability to create biologically plausible sensing solutions. While these platforms continue to improve in regards to latency and power consumption, within recent literature on tactile texture classification there is an emphasis on accuracy at the expense of real-time processing. In order for these tactile sensing systems to find use outside of experimental laboratory environments, it is key to design systems capable of capturing and processing data in real-time. Within this paper we present a system for the real-time classification of texture using a neuromorphic tactile sensor, a spiking neural network and a novel decision making algorithm. Our real-time system achieves classification accuracies of 94% on a dataset of 11 natural textile textures. Furthermore our system is capable of identifying textures at human-level performance in as little as 84ms. Additionally, benchmarking our system across CPU, GPU and Loihi2 hardware platforms resulted in a 96% reduction in power consumption on the neuromorphic platform. This system out-performed previous work by the authors and the state of art, both in terms of accuracy and classification speed.