I'm not sure if this is an Israeli Thing or a cultural trend. However I remember that years ago whenever we did the blessing of the New Moon (ברכת הלבנה, או ברכת החודש) birkat hachodesh we all used to shake hands when we greeted each other with "Shalom Aleichem".
It has been years since I last shook hands during Birkat Hachodesh. So much so, that I've started to doubt my own memory of the custom in Chutz La'aretz. Is this an Israeli thing, or simply a memory of a custom that never existed?