1. Yes, the way many protesters are going about protesting this conflict is shameful and embarrassing. I agree. They're falling into the lesser-evilism trap by coming down on the side of backing Hamas when in fact, it is possible to protest the polices of the state of Israel or the escalation of the conflict without ingratiating oneself with religious extremists and organizations and entities who promote terror over peace.
2. That said, those who opt for war and escalating conflict rather than pursuing peace exist on the Israeli side as well, and its legitimate to criticize them (as many Israelis do) without joining the Hamas fan club. Criticizing the polices of the Israeli state is not necessarily anti-Israel or pro-Hamas. I think too often, some that are uncomfortable or triggered by any criticism of Israel attempt to silence legitimate criticism by hurling accusations of being 'pro-terrorist' or 'pro-Hamas' or 'antisemitic'. These tend to be those less interested in legitimately seeking peace in my observation, and have the mistaken belief that the idea of terrorism is something that can simply be bombed away.
3. I would argue that the media (at least in the US) is actually overwhelmingly pro-Israel and if anything, pro-Israeli sentiments have far more backing and reach. Politically, the pro-Israel lobby like AIPAC is one of the most powerful and well-financed, and very effective at shaping policies and media messages that are friendly towards Israel and shy away from criticizing it. The media in the US often uses passive voice like '10 Palestinian children died' rather than 'Israeli bombing killed 10 Palestinians Children' in order to soften the accusatory tone and obfuscate Israeli military actions as being the cause of these deaths.
4. There are far worse repercussions in the US for being a vocal critic of Israel than there are a vocal supporter. So essentially, what you advocate for is already reality. Many journalists and students who have spoken out about things they disagree with regarding Israel have faced doxxing, blacklisting from employment and legal harassment from wealthy and prominent backers of Israel: https://www.wsws.org/en/articles/2023/10/18/bill-o18.html
5. Propaganda goes both ways. You call for the media to push back against propaganda. Yet Israel's ability to put out its own propaganda and its intelligence apparatus including its cyber and information warfare capabilities are well-documented and world-class. Perhaps the best in the world. The pro-Israel lobby is also extremely well-funded and many of the media outlets are owned by or have significant shareholders who share very pro-Israel sentiments and bias. They are less willing to 'push back' against propaganda that they favor. This is the problem with the demand that the media should 'push back' against propaganda. Do you really want them to push back on all propaganda, or only the propaganda you don't like? The reality is, the media (at least in the US) is mostly pro-US/pro-Israel propaganda with close ties to the US military and intelligence apparatus as well. This is not a conspiracy theory. CIA influence campaigns within the media throughout the years is well-documented. CNN even helped the Pentagon stage fake 'live' broadcasts during the Gulf War to confuse the Iraqi Army. Sure, you might jump up and down and cheer for this and call it a clever intelligence coup. But, it is contrary to your demands that the news should be impartial and push back against propaganda. Frankly, I don't think it's possible to to have purely objective and unbiased media when it is privately owned by wealthy individuals and highly corporatized as most is (at least here in the US). Sure, there's a 'liberal' bias in some newsroom and a 'conservative' bias in others, but neither rarely challenge ideas like the supremacy of the US Empire, its client states, or concepts like the 'righteous use' of Western military power.
6. Arguably, this article of yours is propaganda too, pushing a certain viewpoint. Should it be discredited?
7. Israel (with US backing) commits atrocities as well. These are merely dismissed away as 'collateral damage' and blamed on the enemy though, because the narrative in the West is that the West can do no evil, and any it does is solely in response to attacks on it. This propaganda narrative relies on a flagrant and willful ignoring of a long history of Western imperial powers like the US, Great Britain and their proxy/client actors meddling, occupying, attacking, conquering, and destabilising countries and regions they wish to exploit for their own benefit.
8. There are plenty of 'movements' and factions within Israel that also promote violence, terror and the destruction of Palestinian lives and livelihoods, especially the harassing and terroristic tactics employed by illegal settlers to push out and displace Palestinians from their land in areas like the West Bank and Hebron. Just the other day, violent settlers sabotaged the Olive harvest, burning several groves of Olive trees and depriving Palestinians of their livelihoods: https://yris.yira.org/column/israels-campaign-against-on-Palestinian-olive-trees/ Violent settlers also kill Palestinian livestock, poison wells, and constantly harass and attack Palestinians in the West Bank. Jewish extremists also engage in terrorism, like the 1994 Mosque attack in Hebron that left 29 dead and 125 wounded: https://en.wikipedia.org/wiki/Cave_of_the_Patriarchs_massacre . In the interest of not turning blind eyes, one should not be turned to this fact too, which is a large impediment to the peace process and a 2-state solution, just as Hamas is. In fact the illegal settlement building and ongoing encroachment into Palestinian lands is openly promoted by these factions in Israel as a sabotage tactic to ensure that a 2-state solution is increasingly impossible to achieve due to their entrenchment and positioning in a way that intentionally disrupts the continuity of Palestinian land and communities.
9. I find it ironic that while claiming that Israel is a democratic country more moral than Hamas and its enemies, your solution to addressing protestors saying things you don't like is to fine and jail them. I don't know what Israel's position on free speech is, but this is antithetical to American ideals where political free speech is protected. Granted, the US has failed many times to preserve this freedom (especially in times of war when war protestors come under attack by the police or troops, especially during Vietnam). But... If this is really the 'Israeli' approach to dealing with people who voice opinions you don't like, I'm not sure that's a position worth backing. I don't like what many people write, but I will never advocate their imprisonment for writing it. Sometimes, people are going to exercise their rights and freedoms by doing and saying things you don't like or agree with. That's the reality of living in a free society. If the pro-Israel 'you must not speak ill of Israel' crowd are the sort of people that want to throw people in jail for speech, then I'm not sure how that's any better than other tyrannical regimes like Russia, or Iran that does the same for 'blasphemy'.
10. Disrupting society, promoting lies, destroying property and violent behavior are all things several right-wing Israeli political parties and their supporters have done (including Likud) and are currently doing with little or no serious repercussions or consequences. Perhaps they should be held to the same standards and consequences you propose for 'pro-Palestinian' protestors: https://en.wikipedia.org/wiki/Far-right_politics_in_Israel