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Symmetry-protected spectral topology in non-Hermitian systems has interestingmanifestations such as dynamically anomalous chiral currents and skin effect.We study the interplay between symmetries and disorder in a paradigmatic modelfor spectral topology - the non-reciprocal Su-Schrieffer-Heeger model. Wenumerically study the effect of disorder in on-site and non-reciprocal hoppingterms. Using a real-space winding number, we investigate the impact of disorderon the spectral topology and the anomalous chiral modes under periodic boundaryconditions. We discover a remarkable robustness of chiral current underdisorder. The value of the chiral current retains the clean system value, isindependent of disorder strength and is tracked completely by the real-spacewinding number for class A which has no symmetries, and class AIII, which has asub-lattice symmetry. In class $D^\dagger$, which has $PT$-symmetric on-sitegain and loss terms, we find that the disorder-averaged current is not robustwhile the winding number is robust. We study the localization physics using theinverse participation ratio and local density of states. As the disorderstrength is increased, a mobility-edge phase with a finite winding appears. Theabrupt vanishing of the winding number marks a transition from a partiallylocalized to a fully localized phase. Under open boundary conditions, weobserve a series of transitions through skin effect-partial skin effect-no skineffect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE)for different symmetry classes, where the system without skin effect develops adisorder-driven skin effect at intermediate disorder values. Remarkably whileNHASE is present for different classes, the real-space winding number shows adirect correspondence with it only when all symmetries are broken.

Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension