I think "distasteful" it kind of a moot point when talking about Tom Lehrer's work. See: Poisoning Pigeons in the Park, Masochism Tango, I Hold Your Hand in Mine, etc.
I love his simple charisma. Ever flashy, just charming. In magic there's a form of magic in between close up magic and stage magic called "parlor magic". I've always thought he had great parlor presence.
On a separate note, I find it interesting that he's making casual jokes about himself being gay/bi. I don't know what the times were like, or really even when that video was made, but do wonder if that raised a few (more, I guess) eyebrows
