I would suggest to you that the focus on Iran is because Iran is perceived as being an obstacle to Israeli hegemony in the region and thus undisputed Israeli rule over Palestinian territory.
Iran also justifies its actions in terms of standing up for Palestinians.
So yes, it's very much related.
Most importantly, both groups exist as a direct result of Israeli persecution of their civilian populations. They weren't created by Iran, they're a predictable result that happens when you occupy people's land and oppress them, you get resistance groups.
Netanyahu and his ilk realized that rather than a rapidly moderating, rapidly gaining sympathy and support PLO was not the enemy they "needed" for their own agenda - "from the river to the sea", which, let's not forget, was actually Likud's official election slogan in the 70s and 80s (a "hilarious" irony when certain people try to point to Palestinian usage of this as a "gotcha" - "See, they want to exterminate us!"), and that IDF intelligence showed that Hamas was likely to be more extremist and thus garner more sympathy for Israel, so Israel started supporting Hamas' rise.
As a reminder: Shia are a minority in Lebanon; it's not even close.
The Palestinians are merely a tool for Iran to gain influence, Hezbollah and Shias in Iraq were far more important for them historically
you say that as if israel doesn't have the exact same ideology against iran (it does)
What are the parallels in Israeli society for Iranian school systems morning chants of "Death to Israel" and a public countdown clock to the destruction of Israel?
This could mean anything from a couple of ghettos to all of the modern state of Israel depending on what you think Palestinian territory is or should be.
If you take the approach that all of it is Palestinian territory and the state of Israel shouldn't exist, then yeah, sure? that's different from the assertion that all of the intelligence related businesses in Israel are founded because of direct experience in conflict with the Palestinian people.
You know there's such a thing as internationally recognized Palestinian territory occupied by Israel, right?
Start with that, instead of deploying the 'do you want Israel to not exist' deflection tactic.
Maybe I have a wrong read on the situation between Iran and Israel. But my impression is that Israel is more concerned with Iran as a general threat, moreso than they are concerned that Iran will intervene on behalf of Palestinians, current Palestinian territory, or Hamas.
If Iran didn't get involved directly after ~2 years of open warfare and inarguably genocide-shaped atrocities carried out on civilians, what are they waiting for? Meanwhile Netanyahu has been talking about the danger of Iran developing nuclear weapons for decades now.
Keep in mind I was responding to a post about an assertion that there are so many military startups in Israel because so many Israelis, in their IDF service, have hands-on experience fighting against and oppressing Palestinians. I responded to a post that seemed reductive and misleading in support of that perspective.