I think it's a sore loser being a sore loser. The guy's a jerk, and he's done it before. Other than that, I don't see any religious component to it. FYI, the first time appears to have occurred in May of 2011.
[video=youtube_share;gXNacDRuZUM]http://youtu.be/gXNacDRuZUM[/video]
At 1:01, he bows to his competitor.
At 1:04, his competitor bows back to him.
At 1:05, he turns and begins to stalk off the mat, obviously upset over losing. At the same moment, his competitor begins to walk towards him; if you play the video frame-by-frame, when his competitor stretches out his hand to shake hands, he has completely turned away and clearly cannot see the hand being offered.
The judge is obviously offended by his stalking off the mat, and orders him back. At 1:19, he reappears, bows very slightly to his competitor, and immediately turns and stalks off again, this time clearly ignoring his competitor.
In the most recent match, he won instead of losing, but he's still a jerk. He does bow to his competitor; in the earlier match, he bows deeply; in the more recent match, it's perfunctory. But he does bow. For whatever reason, though, he doesn't shake hands. My question would be whether he shakes hands with anyone. I've seen more than my share of elite athletes who felt it beneath them to shake hands after a game; even in the USA.
The fact is, Egyptians tend not to like Israelis and vice-versa. Although in this case the Israeli competitors were clearly better sportsmen.
Other than that, I think it's a lot of noise over some jerk behaving like a jerk. As to what his fellow Egyptians have to say about it, I'm not surprised. Big deal, they don't like Israel. Huge shocker.
EDIT: I found some other videos of Ramadan Darmish on Youtube. Apparently, he does shake hands with competitors. Just not Israelis. He is a jerk and a poor sportsman.