The point of the proviso was, I would have thought, to stop the castaways from making the boring- and personally unrevealing, choice of either of the two shibboleths. It had little to do with reinforcing cultural norms (which is how the tut-tutters read it) and everything to do with keeping the programme lively. But things have changed. The Bible has lost its hold over us (No foundations trembled when castaway David Walliams said he didn't want it because he didn't like it) and a candidate who chose it now would be revealing something quite interesting about themselves- if only a certain courage and willingness to go against the grain,
I say, Drop it.
Notice that no-one has suggested dropping Shakespeare. (Hooray!)
I've often wondered what my desert island book would be- and I still don't know. I'm not someone much given to re-reading favourite texts. Do you think it would be cheating to ask for the whole of La Comedie Humaine?