the person on the other end actually meant it exactly as rude

Yes.

My response, if somebody is escalating such a thing so much: I allow him, politely and very formally, not to read anymore what I have written in the future. While it is kinda superficial (because everybody has that possibility at all times), it also suggests the possibility to him that he does not need to react in such a strong manner, or that he may even shut up :)