  We study the integer quantum Hall plateau transition using composite fermion
mean-field theory. We show that the topological $\theta = \pi$ term in the
associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124
(2019)] is stable against a certain particle-hole symmetry violating
perturbation, parameterized by the composite fermion effective mass. This
result, which applies to both the Halperin, Lee, and Read and Dirac composite
fermion theories, represents an emergent particle-hole symmetry. For a disorder
ensemble without particle-hole symmetry, we find that $\theta$ can vary
continuously within the diffusive regime. Our results call for further study of
the universality of the plateau transition.
