I am posting this here not just to share my thoughts, but also so that I have an easy place to copy-paste my answer from.
As a context, many libertarians disagree with Israel's 'right to defend itself', because according to them, it exists on a land stolen from Arabs in 1948, when 'Palestinian Arabs' left or were expelled from their lands. This is not the place to address that claim (and I don't have all the facts -- and neither do most people -- and if I did, there are many nuances to consider). What I am addressing here is Israelis' right to defend themselves, either individually or collectively through the organization called State of Israel (or IDF). I am also addressing the claim that the media are not one-sided.
The media are one-sided. You can call it antisemitism or whatever label you want. Perhaps it's cheering for the "underdog" gang-like terrorists vs. the mighty state of Israel (perhaps that's also the reason why libertarian analysis is so one-sided).
Palestinians do not deal with the same thing. They have to deal with the collateral damage produced by IDF killing criminals hiding in the Palestinians' midst (with the latter ofentimes knowingly hiding them). We can argue whether Israel is a criminal organization to its own citizens by the virtue of being a state. We can also argue that perhaps injustice has happened over 60 years ago when people were displaced, or when displaced people were not allowed to return to their homes. Some might argue that injustice did not happen, and it was their fault for siding with Israeli enemy and allowing it to use their territories. Or that now, after all has been said and done, things have changed and people settled on those lands — so, the best solution is to give the displaced people recompense for their lost lands, as resettlement is not an option. Or we can argue that a resettlement must happen.
But this dispute can be solved in a civil manner. Through international arbitration, diplomacy, economic pressure, etc. It cannot be solved through Palestinian thugs shooting rockets at Russian immigrants who came to the country in the 1990s and settled in Sderot.
Imagine if I had a dispute with you over some land. You claim I stole it. I claim otherwise -- that I took it from you justly. Then a third-party tenant settled in the disputed land. If you bomb his house or shoot at his children, and I defend them by shooting back at you, *in that act* (i.e., aside from my previous presumed injustice to you) am I being a criminal? Or are you being a criminal? I think most civilized people would say the latter. And if, through shooting at you I happen to kill some bystanders (especially who willingly hid you in their midst), I don't think you can say that the bystanders are undergoing ethnic cleansing or that they are going through the same thing as the tenant's children.
If you answer to the tenant's complaint that he is living on a stolen land, his answer would be: "Let's settle this dispute in a civilized, peaceful manner through arbitration, but first, the violence must stop."