The mass and spin estimates of the 4U 1636-53 neutron star obtained by the Resonant Switch (RS) model of high-frequency quasi-periodic oscillations (HF QPOs) are tested by a large variety of equations of state (EoS) governing the structure of neutron stars. Neutron star models are constructed under the Hartle?Thorne theory of slowly rotating neutron stars calculated using the observationally given rotational frequency f_{rot} = 580 Hz (or alternatively f_{rot} = 290 Hz) of the neutron star at 4U 1636-53. It is demonstrated that only two variants of the RS model are compatible with the parameters obtained by modelling neutron stars for the rotational frequency f_{rot} = 580 Hz. The variant giving the best fit with parameters M similar to 2.20 M_{Sun} and a similar to 0.27 agrees with high precision with the prediction of one of the Skyrme EoS. The variant giving the second best fit with parameters M similar to 2.12 M_{Sun} and a similar to 0.20 agrees with lower precision with the predi