We present DeepCSI, a novel approach to Wi-Fi radio fingerprinting (RFP) which leverages standard-compliant beamforming feedback matrices to authenticate MU-MIMO Wi-Fi devices on the move. By capturing unique imperfections in off-the-shelf radio circuitry, RFP techniques can identify wireless devices directly at the physical layer, allowing low-latency low-energy cryptography-free authentication. However, existing Wi-Fi RFP techniques are based on software-defined radio (SDRs), which may ultimately prevent their widespread adoption. Moreover, it is unclear whether existing strategies can work in the presence of MU-MIMO transmitters - a key technology in modern Wi-Fi standards. Conversely from prior work, DeepCSI does not require SDR technologies and can be run on any low-cost Wi-Fi device to authenticate MU-MIMO transmitters. Our key intuition is that imperfections in the transmitter's radio circuitry percolate onto the beamforming feedback matrix, and thus RFP can be performed without explicit channel state information (CSI) computation. DeepCSI is robust to inter-stream and inter-user interference being the beamforming feedback not affected by those phenomena. We extensively evaluate the performance of DeepCSI through a massive data collection campaign performed in the wild with off-the-shelf equipment, where 10 MU-MIMO Wi-Fi radios emit signals in different positions. Experimental results indicate that DeepCSI correctly identifies the transmitter with an accuracy of up to 98%. The identification accuracy remains above 82% when the device moves within the environment. To allow replicability and provide a performance benchmark, we pledge to share the 800 GB datasets - collected in static and, for the first time, dynamic conditions - and the code database with the community.