  We study hybrid stars considering the effects on stellar stability of the
hadron-quark conversion speed at the sharp interface. The equation of state is
constructed by combining a model-agnostic hadronic description with a constant
speed of sound model for quark matter. We show that current LIGO/Virgo, NICER,
low-density nuclear and high-density perturbative QCD constraints can be
satisfied in two scenarios, with low and high transition pressures. If the
conversion speed at the interface is slow, a new class of dynamically stable
hybrid objects is possible and very stiff hadronic equations of state cannot be
discarded. Densities tens of times larger than the nuclear saturation density
are possible at the center of these objects. We discuss possible formation
mechanisms for the new class of hybrid stars and smoking guns for their
observational identification.
