  The Resonant Switch (RS) model of twin high-frequency quasi-periodic
oscillations (HF QPOs) observed in neutron star binary systems, based on switch
of the twin oscillations at a resonant point, has been applied to the atoll
source 4U 1636-53 under assumption that the neutron star exterior can be
approximated by the Kerr geometry. Strong restrictions of the neutron star
parameters M (mass) and a (spin) arise due to fitting the frequency pairs
admitted by the RS model to the observed data in the regions related to the
resonant points. The most precise variants of the RS model are those combining
the relativistic precession frequency relations with their modifications. Here,
the neutron star mass and spin estimates given by the RS model are confronted
with a variety of equations of state (EoS) governing structure of neutron stars
in the framework of the Hartle-Thorne theory of rotating neutron stars applied
for the observationally given rotation frequency f_rot~580 Hz (or alternatively
f_rot~290 Hz) of the neutron star at 4U 1636-53. It is shown that only two
variants of the RS model based on the Kerr approximation are compatible with
two EoS applied in the Hartle-Thorne theory for f_rot~580 Hz, while no variant
of the RS model is compatible for f_rot~290 Hz. The two compatible variants of
the RS model are those giving the best fits of the observational data. However,
a self-consistency test by fitting the observational data to the RS model with
oscillation frequencies governed by the Hartle-Thorne geometry described by
three spacetime parameters M, a and (quadrupole moment) q related by the two
available EoS puts strong restrictions. The test admits only one variant of the
RS model of twin HF QPOs for the Hartle-Thorne theory with the Gandolfi et al.
(2010) EoS predicting the parameters of the neutron star $M \sim 2.10
\mathrm{M}_{\odot}$, $a \sim 0.208$, and $q/a^2 \sim 1.77$.
