We systematically explore the relative impact of the Coulomb interaction and the nuclear symmetry energy on the proton and neutron density distributions in the 212Pb + 208Pb, 132Sn + 124Sn and 54Ca + 48Ca central collisions at beam energies below 800 MeV/A. The Boltzmann-Uhlenbeck-Uehling (pBUU) transport and the Time-Dependent-Hartree-Fock (TDHF) frameworks with SV-bas and SV-sym34 Skyrme parametrizations are employed. Maximum total particle number density and the proton-neutron (isospin) asymmetry have been calculated as a function of beam energy, system size and the Skyrme model, with and without the Coulomb force for all systems. The maximum total density, overall not exceeding 2.5-3.0ρ0 (ρ0=0.16fm−3), is observed to be lowered by the Coulomb interaction by less than 10%. The maximal asymmetries are not enhanced but decreased in the reaction as compared to the initial state in the majority of cases, and lowered by up to 45% due to the Coulomb effects. Furthermore, the proton and neutron density distributions in the plane transverse to the beam direction have been modelled. The distributions are found to vary throughout the reaction space, with the Coulomb force increasing the isospin differences closer to the center of the collision. The general conclusion of this work is that the Coulomb interaction plays a significant role in the collision dynamics, and enhances the rather weak response of the colliding systems to the nuclear symmetry energy and its density dependence. Thus, inferring symmetry energy from comparing theory and data requires careful modelling of Coulomb effects, in addition to nuclear, in any reaction simulation.