We investigate neutron star solutions in scalar-tensor theories of gravity with first-order derivative self-interactions in the action and in the matter coupling. We assess the robustness of the kinetic screening mechanism present in these theories against general conformal couplings to matter. The latter include ones leading to the classical Damour-Esposito-FareĢse scalarization, as well as ones depending on the kinetic term of the scalar field. We find that kinetic screening always prevails over scalarization and that kinetic couplings with matter enhance the suppression of scalar gradients inside the star even more, without relying on the nonlinear regime. Fine tuning the kinetic coupling with the derivative self-interactions in the action allows one to partially cancel the latter, resulting in a weakening of kinetic screening inside the star. This effect represents a novel way to break screening mechanisms inside matter sources and provides new signatures that might be testable with astrophysical observations.
