Smart textiles have found numerous applications ranging from health monitoring to smart homes. Their main allure is their flexibility, which allows for seamless integration of sensing in everyday objects like clothing. The application domain also includes robotics; smart textiles have been used to improve human-robot interaction, to solve the problem of state estimation of soft robots, and for state estimation to enable learning of robotic manipulation of textiles. The latter application provides an alternative to computationally expensive vision-based pipelines and we believe it is the key to accelerate robotic learning of textile manipulation. Current smart textiles, however, maintain wired connections to external units, which impedes robotic manipulation, and lack modularity to facilitate state estimation of large cloths. In this work, we propose an open-source, fully wireless, highly flexible, light, and modular version of a piezoresistive smart textile. Its output stability was experimentally quantified and determined to be sufficient for classification tasks. Its functionality as a state sensor for larger cloths was also verified in a classification task where two of the smart textiles were sewn onto a piece of clothing of which three states are defined. The modular smart textile system was able to recognize these states with average per-class F1-scores ranging from 85.7 to 94.6% with a basic linear classifier.