The link above has a good discussion of anti-Israel media bias. It has hit home because I used to be affected by the same bias myself, and description is quite close to my own experience – except for the fact that I never personally witnessed things described in the article, with main factor in my own change of heart being learning about Islam itself. Also, I was never really a liberal myself. I was a socialist at times, but due to history of my nation (being from Croatia), I always was a nationalist. And that is a danger of knowing facts without context. It is a fact that Israel is bombing Palestine: but context is that they are only doing it in self-defense. It is a fact that Europe had colonized Islamic world: but context is that said colonialism was merely an act of self-defense against Islamic aggression. It was very successful self-defense as well, forcing Islam to fight against infidels on its own home turf, instead of coming over to fight in Europe.
Today, Islam is carrying out aggression against both Israel and Europe, through a combination of terrorist cells and mass immigration. How this war will end, nobody knows. And Israel, with hostile Arabs in front and hostile, increasingly Islamic liberal Europe in the rear, is in dire straits. Both Islam and liberalism are dogmatic, illogical sets of beliefs, and are working together to destroy Europe. Left reacts with outrage whenever West attempts to protect itself against Islam, and so acts as a Trojan horse enabling Islamic conquest. Israeli “colonization” of Palestine works under the same logic as European colonization of Africa and the Middle East: it creates a tampon zone to protect Israel itself from Islamic aggression, and moves the violence to Islam’s home turf. Islam has an inbuilt hatred against all non-Muslims, but this hatred is especially pronounced against the Jews. Palestinian terrorists intentionally use civilians as human shields in order to make Israel look bad in the eyes of emasculated liberal West.
Liberal West itself uses double standards: what is acceptable for Muslims to do, is not acceptable for Israelis to do. Reason for this is inbuilt liberal anti-white, anti-Western racism: they see conflict as a developed Western country beating on underdeveloped Arab neighbour because it fits their narrative of Westerners always being the oppressors. When facts cannot be made to fit the narrative, they deny the facts, positing that Islamic terrorism is not endemic to Islam, but is in fact created by the West.
A reading that may help explain causes of liberal antisemitism: “Nazi roots of multiculturalism“