It's not an issue of Islamic countries - Lebanon isn't one by any stretch and this is looking like a bit of a freak thing. They got pinched in one of the safer areas, which happens to be near a training camp for a Palestinian group that has acted on Syria's behest before. The newspapers are mostly explaining it as a ransom but word is that they were identified at the Syrian border as good targets and word was passed to the Palestinian group, who pinched them to be held as some kind of insurance in case there was an international intervention against Syria.

The Daily Star is a very reliable newspaper and has a lot of details of this case.
THE DAILY STAR :: Breaking News, Lebanon News, Middle East News & World News

Also, in terms of staying away from crowds, Lebanon is a very different kettle of fish to any of the other ME countries - the (pretty) democratic government generally has a decent amount of consent and it's not likely to experience (or repress) mass protests. The only places to be wary of are one or two of the Palestinian camps (Ain Hilweh is not a nice place, although the camps in Beirut tend to be fine) as well as the security zone in the South (dangerous because of occasional Israeli shelling and cluster bombs).

You won't get into either of these areas without seeking permission from the Army anyway so it's not really a worry, but the south is well worth the trip. Absolutely beautiful mountains and valleys.