IDC is very conservative, so if youre pretty liberal than yes, I would avoid it. I'd only recommend it if you were interested in American/Israeli diplomacy.
I completely disagree with MollyB about needing to dress modestly if you live in Tel Aviv, thats just ridiculous. In Jerusalem or smaller cities yes, you would need to. BUT if you really wanted to gain an intimate understanding of Israel and Palestinian society, and get a well rounded sense of the conflicts and issues in Israel, Tel Aviv is the wrong place to live - its a really modern 'bubble', and its pretty easy to go about your daily life without being confronted with harsh truths.
I agree with MollyB about Israeli universities and studying there. Perhaps consider interning/working at an Israel/Palestinian organization to supplement your degree? There are a TON of activist nonprofits in Israel and Palestine, and they are usually very interested in taking on native english speakers as interns - and would especially be interested in someone who is learning Arabic.