Well I am going to bed now with the cricket on.
For the benefit of Tilly and Corby I shall reprint my original point in politically inert wording so as to make them feel all happy and warm.
To get into Israel you can't (or use to be that you couldn't) have any stamp of Muslim denomination other than Egypt in it and vica versa in travelling the other way around -the only exemption being for the Jerusalem Cairo link. So what one does (or used to do) is fly London - Cairo on a 'Muslim only' passport and have the Israeli passport DHLed out to your Cairo hotel. And then into Jerusalem. If you are travelling on into the M-East, fly back to Cairo and pick your designated 'Muslim countries'-only passport up from the hotel safe back in Cairo.
Yawn yes, joke perhaps yes, necessity to do this and in having two passports yes....and also it applies to some other sensitive countries in the world and visiting them as part of a multi-nation business trip.
(With advice taken from aluminary websites such as the Race Relations Board and the Foreign Office). And also avoiding the use of non-words.