  Because spin-orbit coupling (SOC) is invisible in the band structure when
inversion symmetry exists, whether spins are trivially degenerate or strongly
coupled to momentum due to SOC is presumed to make little difference in
transport measurements, such as magnetoresistance and quantum oscillations. In
this work, however, we show that hidden Rashba SOC in a centrosymmetric
two-dimensional material can lead to the quantum Hall effect with only
even-integer plateaus, unlike a spinless electron gas. Here, two Rashba layers
that are degenerate but with opposite SOC due to inversion symmetry, hybridize
with each other and create two doubly-degenerate bands with hidden spin
texture. Correspondingly, two branches of Landau levels interact, resulting in
significant suppression of spin splitting due to the balancing of intralayer
SOC and interlayer hybridization. Furthermore, we show that breaking inversion
symmetry restores the ordinary quantum Hall fluid by introducing spin-split
Fermi surfaces. Our theory can apply to centrosymmetric materials with strong
SOC, as demonstrated in a recent experiment on the two-dimensional
semiconductor Bi$_2$O$_2$Se.
