Yeah, oxalic acid isn´t meant to be used as skin lotion harsh stuff on skin, not very dangerous I would say, but just dangerous, if smeared on skin or ingested.We used it extensively to remove oxide stains after welding stainless steels.
The one we used was a white paste and if you got something on your skin it went yellow in a short time.
It was very dilute though.
If the acid or base is just a tiny bit lipophilic, then it is much stronger iritant and it is much more corrosive to the tissue, as it can quickly penetrate it. That is why HCl is relatively slow on attacking your skin, and if you wash it off your hands in dozen of seconds, not that much will happen. But if this misfortune will happen to you with acetic acid (concentrated pure stuff, not vinegar), that would be bad... Even tho HCl is in order of 12 magnitudes more strong acid than acetic acid.