If anything the skew within the platforms is to prioritize pro-palestinian views https://twitter.com/committeeonccp/status/173279243496103143...
It also seems like these platforms create (rather than support) anti-Israeli views: https://twitter.com/antgoldbloom/status/1730255552738201854
US views skew pro-israel, and GenZ is closer to 50/50, so if there's something going on online, it's not in favor of Israel.
It's probably relevant that there are 1 billion Muslims to 16 million Jews, and that the largest relevant population of pro-Israeli internationals is India and Indian Hindus, and they are not on TikTok (blocked in India).
I think it is currently about an order of magnitude more civilians deaths have resulted from the actions of Likud (Netanyahu etc..., who control the government and hence the IDF) than from the actions of Hamas. IDF is apparently disrupting civilian aid, destroying infrastructure including hospitals, and causing mass population movements into areas that cannot support them, so the risk of death from starvation and infectious disease at a massive scale as an indirect result is high. The Likud-controlled IDF are also apparently enforcing a 'lock down' of Palestinian civilians in the West Bank while allowing Israeli citizens to seize land by force and further expand the occupied territories.
So the scale of the atrocities seems to be much higher on the Likud side than the Hamas side, covers both the West Bank and Gaza, and it makes sense that the Palestinian victims of those atrocities would receive more support. That doesn't mean that all the people who care about the plight of the Palestinian population are anti-Israel (they are just not posting about it because they are likely prioritising issues).
What I would and do blame the current government for is that Oct 7th even happened, the scale, and the immediate response.
EDIT: I also blame the current government for trying to eliminate any possibility of a two state solution and effectively supporting the Hamas rule in Gaza as means of accomplishing that. I can probably blame them for lots more. That said the actual Oct 7th attack is all on Hamas and the response is pretty much the only response you'd have seen from any Israeli government (or anyone else in that position for that matter). We're in a place today that is a different place and we can talk all we want about what other possible places we could be.
I'll agree with you on the west bank policy being a Likud/right-wing policy in general. We can also talk about why the Israeli public is more right wing leaning and the left has all but disappeared.
I think those two groups are really more mutually exclusive than what you're trying to portray. At least to most Israelis they are. Because for most Israelis, when you say "peaceful within 1967 borders", it reads as "kill all the Jews in Israel". Many (most?) Palestinians will also not accept this statement because they consider Israel in the 1967 border to be the Palestinian state. If there was an overlap we wouldn't really be where we are, we'd have peace. I have not met many people who are in this overlap, i.e. they're both "pro-Israel" and "pro-Palestine" in a meaningful way. Most people do not hold nuanced views at all, don't know that much about the conflict, don't really understand what's going on, hold on to simplistic narratives and "windows" they get from the media and social media. For me as an (ex-) Israeli your equating the response of Israel to the Hamas puts you squarely in the anti-Israeli camp. You blank statement "massacre of civilians under the orders of Likud (and other far right parties)" feels like a blood libel. This is just my emotional response to how you phrase things. So that doesn't seem to be an overlap of pro-israeli and pro-palestinian.