  The high-energy tails of charged- and neutral-current Drell-Yan processes
provide important constraints on the light quark and anti-quark parton
distribution functions (PDFs) in the large-x region. At the same time,
short-distance new physics effects such as those encoded by the Standard Model
Effective Field Theory (SMEFT) would induce smooth distortions to the same
high-energy Drell-Yan tails. In this work, we assess for the first time the
interplay between PDFs and EFT effects for high-mass Drell-Yan processes at the
LHC and quantify the impact that the consistent joint determination of PDFs and
Wilson coefficients has on the bounds derived for the latter. We consider two
well-motivated new physics scenarios: $1)$ electroweak oblique corrections
$(\hat W, \hat Y)$ and $2)$ four-fermion interactions potentially related to
the LHCb anomalies in $R(K^{(*)})$. We account for available Drell-Yan data,
both from unfolded cross sections and from searches, and carry out dedicated
projections for the High-Luminosity LHC. Our main finding is that, while the
interplay between PDFs and EFT effects remains moderate for the current
dataset, it will become a significant challenge for EFT analyses at the HL-LHC.
