Hmm ,,, white petroleum jelly or rod wax (known to many through the
brand name Vaseline) is not what I call a hydrocarbon grease.

But that's the cheap grease on plumbing fittings.

What I call hydrocarbon (or petroleum-based) greases (such as bearing
greases) are soaps of mineral oil.

Right, but those are not for wet applications.

Repeated skin contact with hydrocarbon greases (and petroleum oils) can
lead to dermatitis.

Not in this case. On the contrary, petrolatum is a *remedy* for
dermatitis.