Iran is Shia and not Arab (neither ethnically nor linguistically), so they don't have any intent on showing solidarity with Sunni Arabs. Shia are an oppressed minority throughout most of the Islamic world, Iran is the only significant Shia majority state. Al Qaeda, ISIS have actively attacked Iran and Shias. Hezbollah was a Shia militia formed from self defence groups against Sunni (and christian) groups. Shia muslim groups lived in southern Lebanon, when Israel invaded Lebanon in response to Sunni Palestinian acts, the Shia population were badly affected (including by massacres carried out by Israeli proxy forces) The occupied part of Lebanon was predominantly Shia, so Hezbollah was formed from disparate Shia organisations to become a unified resistance organisation fighting to free Lebanon from Israeli occupation. Iran supported them as co-religionists, and as an anti-colonial movement.
The relationship with Hamas a Sunni organisation is different. Historically Iran under the Shah / US hegemony was allied with Israel. The US and Israel supported the Shah and thus were opposed to the Iranian revolution and the overthrow of the dictatorship imposed on Iran when the US overthrew the democratically elected Iranian government. Philosophically the Iranian revolution had an anti-colonial element, and the struggle of the Palestinian people was seen as an anti-colonial struggle, and the support for the Palestinian resistance is thus a political not a religious issue.
In theory it should be much easier to split Iran from Hamas than Hezbollah, In either case a political solution guaranteeing the freedom and security of Palestinians and Shia Lebanese would effectively end the need for Hamas and Hezbollah as military organisations.
Israel has provoked much sectarian violence, even including some support for ISIS, in particular supporting Christian militias in Lebanon who carried out massacres of Palestinians and Shias. Israel also has funded and armed sectarian terrorist groups in Iran. Israel has also supported Kurdish nationalist groups in Iraq and Syria. So I don't think there is a good case for Israel reducing sectarianism in the middle east.