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We study the statistics of various large-scale structure tracers in gravity-only cosmological simulations including baryons and cold dark matter (CDM) initialized with two different transfer functions, and simulated as two distinct fluids. This allows us to study the impact of baryon-CDM relative perturbations on these statistics. In particular, we focus on the statistics of cosmic voids, as well as on the matter and halo real-space 2-point correlation function and baryon acoustic oscillations (BAO) peak. We find that the void size function is affected at the 1–2 per cent level at maximum, and that the impact is more important at higher redshift, while the void density profile and void bias are roughly unaffected. We do not detect a sizeable impact of relative baryon-CDM perturbations on the real-space correlation functions of matter and haloes or the BAO peak, which is in line with results from previous works. Our results imply that it would be hard to use voids or real-space correlation functions to constrain baryon-CDM relative perturbations, but also that we might not have to include them in models for the analysis of future cosmological surveys data. [ABSTRACT FROM AUTHOR]