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Modern global analyses of the structure of the proton include collider measurements which probe energies well above the electroweak scale. While these provide powerful constraints on the parton distribution functions (PDFs), they are also sensitive to beyond the standard model (BSM) dynamics if these affect the fitted distributions. Here we present a first simultaneous determination of the PDFs and BSM effects from deep-inelastic structure function data by means of the NNPDF framework. We consider representative four-fermion operators from the SM effective field theory (SMEFT), quantify to which extent their effects modify the fitted PDFs, and assess how the resulting bounds on the SMEFT degrees of freedom are modified. Our results demonstrate how BSM effects that might otherwise be reabsorbed into the PDFs can be systematically disentangled.