See below images for what appears to be a girdling root that might eventually start choking off a main root. Before I remove it I wanted to get some thoughts. Any input is much appreciated!
It won't choke the larger root. I would have no hesitation at removing either, or both roots. I live in a forest and have cut roots over 4" diameter with no adverse affect on trees ( southern pines, oaks, fig, sweet gums and others). The limit is how much work you want to put in with an axe as it dulls chain saw blade to run them into the ground. Loppers will easily cut the little root.