That's why there's an entirely separate class of soap products formulated specifically for those among us who own and operate a vagina.
I think people should abandon this heuristic.
For this reason, I stick to either first-generation soap (made by saponification) or simple surfactants.
In general, as a precautionary principle, it is always good to stick to simple products that have been around for a long time.
(Skin is, in general, rather more sensitive to bases than acids. Even a fairly mild base will make skin feel unpleasant and a bit slimy, whereas holding an orange slice (quite acidic) is not particularly irritating to intact skin.)
https://www.sciencedirect.com/science/article/pii/S009167492...
And overuse of soap is definitely irritating to skin — this is not a particularly subtle effect.
And I think it will be neutralized by the acids inside the stomach.
unfortunately googling shows that mixups happen every so often, sometime due to what I’d call gross or willful negligence like storing it in a re-used food container in the fridge