That's interesting, when I was there recently they insisted on stamping my passport, stating they were under specific direction not accept requests to stamp a card. It wasn't a huge issue, as my passport expired very soon after.
Then again, it could be a discriminatory practice, as I entered from the King Hussein crossing (into the West Bank), which is predominantly used by Arabs, as opposed to TLV airport.
Either way, I wouldn't count on it, especially with a trip of this nature!
