I love Israel as a country and culture, but I am very skeptical of what's going on there with the Palestinians. I have a few Jewish/Israeli friends, and political discussions easily turn heated – e.g. on Facebook.
Realistically the Israelis will do a digital background check on anybody entering their country – natural language processing of everything you wrote on Facebook included – they do that because they can, and they can because they are close allies with the U.S.
Is it possible that critical comments on Facebook / forums or maybe even some mild forms of activism beyond Facebook (like financially supporting projects like http://www.breakingthesilence.org.il/) could be reason to be denied entry to Israel?
I think this would be pretty harsh, but knowing some Israelis, it seems they have little patience with foreigners expressing political skepticism. And also judging from the tense atmosphere answering those questions at the border, I would not be too surprised if they don't hesitate to refuse people they don't like.
http://www.theguardian.com/world/2013/sep/11/nsa-americans-personal-data-israel-documents