Media bias on Israel has a few motivation/reasons... among them: 1) radical liberalism (including by Jews who fail to see the enemy), 2) Arab Muslim goliath influence.
Anti-Israel bias is present on both the far left and the far right. Support of Israel has never broken down along left vs. right lines.
I can give you a nice long list of even mainstream Republicans who are anti-Israel, starting with Brent Scowcroft. It’s a pretty long list if you want it, probably every bit as long as the similar list of Democrats. I can also list some pretty hard left Democrats who are staunch supporters of Israel and, of course, I can do the same for conservative Republicans.
I think age old anti-Semitism in Europe and the Middle East is much more of a culprit than either cause you mention. Also, of course, some on the far left see the Palestinians as underdogs and always root for what is perceived as the weaker side, ignoring the support the Palestinians get from Iran and the Arabs. I also think the anti-Israel bias in many liberal colleges and universities has brainwashed a lot of these reporters who know little or nothing of the actual history of the region.
It’s all too easy to try and pigeonhole the bias. I’d rather speak up against it rather that try to classify, box and label the people who do it.