Are people forgetting that Israel is the only democracy in the Middle East? The US enjoys a very healthy military relationship with Israel because of its advanced technology and its strategic location....all religion aside.
One problem is that it's difficult to consider the question of Israel being a "democracy" while setting aside "all religion". (Short version: there are a lot of people in occupied territories that don't have a vote.)
Another is that there is a very good question of just how much can you let a country get away with just because they are or claim to be a democracy? That amount is surely limited (right?), but the question is, how much?
Yes they do. In their own government(s). What are you talking about?
Edit: Oh gosh... downvoted? I feel as though I am on reddit.
Edit 2: They voted for Fatah and Hamas. They do get to vote - in their own elections. (Though not for a few years because Hamas and Fatah have postponed elections multiple times)
By your logic, the United States is not a democracy because illegal aliens cannot vote in US elections.
What happened to Turkey?
According to that Israel is a 'Flawed democracy' and Lebanon is a 'Hybrid regime'. I cannot say I'm familiar with the political system in Lebanon, but I do know they've been having some major issues with their government lately. IIRC they haven't had a functioning executive branch since they agreed to comply with the UN investigation into the assassination of former Prime Minister Rafiq Hariri. Hezbollah (effectively the military of Lebanon and a very strong political power) is extremely unhappy with this because the allegation is that they assassinated him.
[1] quick googling turned for example http://fullcomment.nationalpost.com/2011/04/01/full-comment-...
[2] due to time constraints I can't find recitations now, so take it at face value. Sorry.
EDIT: eh, life just gave a brilliant new example: http://blogs.telegraph.co.uk/news/michaelweiss/100092061/bre...