I don't know about respectable, but I prefer car/cdr even in a new Lisp. In addition to the composability of the notation, which others have cited, there's the clear lexical symmetry between the two; their compactness, which adds value when writing and reading concise programs; and how easy they are to say out loud. There's something also about their precision: when you say 'car' or 'cdr' in a Lisp context it's immediately clear that there's a linked list at hand and you're talking about it.
The main disadvantage is that they're words with no immediate connection to their meaning, but that's true of many words we're all familiar with. It really only costs anything in the learning stage—which admittedly is a critically important stage. But I think it's fair for a programming language to use specialized idioms for a small number of their most fundamental constructs.
CAR and CDR are also good names because they are part of the Lisp tradition. Also due to this tradition, they have a clear meaning in the context of Lisp. If the "new Lisp" keeps conses (and some may argue that if it doesn't, it shouldn't really fall under "a Lisp"...), perhaps it should also keep these names.
The main disadvantage is that they're words with no immediate connection to their meaning, but that's true of many words we're all familiar with. It really only costs anything in the learning stage—which admittedly is a critically important stage. But I think it's fair for a programming language to use specialized idioms for a small number of their most fundamental constructs.