Topological phases exhibit properties that are conserved for continuous deformations, as demonstrated in topological protections in condensed-matter physics and electromagnetic waves. Despite its ubiquitous nature and recent extensions to synthetic dimensions, non-Hermitian Hamiltonians, and nonlinear dynamics, topological protection has generally been described in spatial lattices with the Chern number in the Brillouin zone, focusing on the realization of backscattering-free wave transport... Here, we investigate a different class of topological protection in parity-time-symmetric nonlinear optical dynamics, exploiting the topological invariance of optical state trajectories. For coupled nonlinear photonic systems composed of gain and loss atoms, we classify the topology of equilibria separately for unbroken and broken parity-time symmetry. Utilizing the immunity of topological phases against temporal perturbations, we develop noise-immune laser modulation and rectification with a parasitic nonlinear resonator based on oscillation quenching mechanisms that are protected by parity-time symmetry. The connection between topological photonics and parity-time symmetry through nonlinear dynamics provides a powerful platform for noise-immune signal processing. (read more)