Context. Spacecraft data revealed early on the frequent observation of multiple near-thermal proton populations in the solar wind. Decades of research on their origin have focused on processes such as magnetic reconnection in the low corona and wave-particle interactions in the corona and locally in the solar wind. Aims. This study aims to highlight the fact that such multiple thermal proton populations and beams are also produced by magnetic reconnection occurring locally in the solar wind. Methods. We used high-resolution Solar Orbiter proton velocity distribution function measurements, complemented by electron and magnetic field data, to analyze the association of multiple thermal proton populations and beams with magnetic reconnection during a period of slow Alfvénic solar wind on 16 July 2020. Results. At least six reconnecting current sheets with associated multiple thermal proton populations and beams, including a case of magnetic reconnection at a switchback boundary, were found on this day. This represents 2% of the measured distribution functions. We discuss how this proportion may be underestimated, and how it may depend on solar wind type and distance from the Sun. Conclusions. Although suggesting a likely small contribution, but which remains to be quantitatively assessed, Solar Orbiter observations show that magnetic reconnection must be considered as one of the mechanisms that produce multiple thermal proton populations and beams locally in the solar wind.