We present an analysis of the matter, halo and galaxy clustering in $f(R)$-gravity employing the SHYBONE full-physics hydrodynamical simulation suite. Our analysis focuses on the interplay between baryonic feedback and $f(R)$-gravity in the matter power spectrum, the matter and halo correlation functions, the halo and galaxy-host-halo mass function, the subhalo and satellite-galaxy count and the correlation function of the stars in our simulations. Our studies of the matter power spectrum in full physics simulations in $f(R)$-gravity show, that it will be very difficult to derive accurate fitting formulae for the power spectrum enhancement in $f(R)$-gravity which include baryonic effects. We find that the enhancement of the halo mass function due to $f(R)$-gravity and its suppression due to feedback effects do not show significant back-reaction effects and can thus be estimated from independent GR-hydro and $f(R)$ dark matter only simulations. Our simulations furthermore show, that the number of subhalos and satellite-galaxies per halo is not significantly affected by $f(R)$-gravity. Low mass halos are nevertheless more likely to be populated by galaxies in $f(R)$-gravity. This suppresses the clustering of stars and the galaxy correlation function in the theory compared to standard cosmology.