Historically the Shia's have been a minority and have often played by the rules of assymetric warfare. As I learned from a tv documentary, we get the word "assasin" from an early small Islaimi Shia group (the Nizaris) which fought against the larger Sunni group by killing its leaders.
The best solution for that whole region is more secular governments. That will not happen because the only one is Jewish. The only other thing is to be neutral in this whole sunni-shia divide. If they want to fight and kill over whether to follow the son-in-law or father-in-law of muhammad we cannot stop them but the US should not be a part of it. If that means giving some leeway to Iran I think we should do that instead of coming exclusively on the side of Sunni arabs.
More secular governments would be a good thing, but that's not really going to happen. See Shadi Hamid's writings on the matter. Essentially, the future of the Muslim Middle East is more illiberalism and more Islamism.
As you mentioned, currently the only democracy in the ME is Israel, though I have hope for a secular and democratic Kurdistan. I've heard whispers that the main reason the US isn't backing an independent Kurdistan separating from Iraq is the worry that the lack of the Kurds as a moderating force on Iraq will enable Iran to fully control the state (more so than it already does), essentially allowing it to become an Iranian client state.
Being neutral in the Sunni-Shi'a divide is functionally impossible for a number of reasons, but to easily understand why it's impossible, just try to imagine what neutrality in that context would actually look like. There's no answer that all sides would agree is neutral. The US has to be a part of it because the US has no choice - Americans benefit from the US dominated world order (as do most other people of the world). When you're a superpower with stakes in virtually every matter, even inaction is an action; even not choosing is a choice.
Enabling Iran hurts American interests. Iran is a destabilizing force, rather than a status quo power. Iran has had, and continues to have a choice: is it a movement, or is it a respectable state? It's leaders have consistently chosen to be a movement, exporting its revolution wherever it can, and upending the region and the world according to its vision. And let's not forget, a part of that vision is the annihilation of America's one reliable ally in the region, Israel, and the murder of all of its Jewish inhabitants.
We can only say that Iran acts rationally if we understand its motives. Its leaders view power and geopolitics as a zero-sum game, and it cannot win as long as the US, Israel, and the Sunnis are not dominated by its Shi'a axis.
I agree with what you say about Iran but I think the US should still engage in order to make inroads with moderates there. International pressure has worked in Iran and a large country like that does feel the pressure. 3 million protestors in 2009 is a big deal. They now have more more moderate presidents and foreign ministers. I think the US should support Israel and also be as neutral as possible in the Shia-Sunni conflict which is coming more to the forefront. The US will be active in that part of the world because of supporting Israel, but we have to be smarter. There have been too many mistakes. Recently I think meddling in the Syrian conflict was also a mistake which can rightly be seen as pro-Sunni.
When we say that we should engage with the moderates in Iran, it all sounds nice and dandy. But when we get to the nitty-gritty of the matter, it becomes more difficult to identify when we're engaging with moderates and when we're getting the fleece pulled over our eyes, since the moderates are systemically beholden to the Ayatollah and his 'guardians of the revolution'. I wish the Obama administration had done more to support the Green revolution protesters in 2009, but those days seem to be over, and ever since the regime has worked hard to disempower, co-opt, or placate the protestors and/or their supporters.
I don't actually think that the Rouhani administration is any more moderate than the hardliners - just more strategic. Their goals align with the conservatives goals, but they are more willing to take a conciliatory tone with the West, even if it is only tone and not strategic realignment. So, then if it's just a matter of how to achieve hegemony - whether by direct conflict (hardliners) or subversion and manipulation of the West (Rouhani), does it really benefit the West to empower the moderates? Obviously, I think not. Besides, the Rouhani government is also just acting as political cover for Iran's other operations, whereby Rouhani and Zarif play good cop, while the IRGC and alike play bad cop.
The Sunni status quo powers (which does not include Qatar) are in de facto alignment with Israel because the biggest threat to both is the Iranian destabilization (mostly via proxy forces). Iran understands that if its actions empower Sunni radicals to the detriment of relatively moderate Sunnis, Iran wins, because then it positions itself as a bulwark against radical Sunni Islamism - even if its actions help create the environment conducive to those forces gaining strength.
As for 'meddling' in the Syria conflict being pro-Sunni, I just disagree. The Assad regime is the biggest draw for Sunni violent extremism, and the longer Iran enables Assad's slaughter of his people, the biggest the problem is going to be for the West.
I agree with a lot of what you are saying and you know a lot about the situation. However if the Rouhani administration is strategic and its goals align with not having nuclear weapons then the international community should accept it strategically as well. Rouhani is indeed nothing more than a well dressed Islamic militant, but I don't think the other Sunni leaders are any better, even if they are also strategically allying with the US policies to further their objectives too.
As for Syria I completely disagree, this version that Assad is slaughtering his people as if he is another demon with nothing better to do is just more US propaganda. He was fighting rebels but was just not careful and there are many civilian casualties. We don't need another headless state for radicals to occupy. The US meddled in Iraq, Libya and now is strengthening ISIS even more by destroying the sovereign nation (Syria) that is fighting it. If the US has a problem with Syria, then Congress should debate and then declare war on it. Talk of no-fly zones is ridiculous. We only don't like Syria because they are close to Iran. Saudi has reportedly pumped $700 million into rebel groups. Supporting these Sunni extremists and then claiming to also fight ISIS is foolish. Saudi and their coalition are attempting to establish their Sunni Islam across the middle east. And that is not better than Iran. At least in Congress Tulsi Gabbard is the one congressperson saying we need to let Assad stay and focus efforts on ISIS.
The best solution for that whole region is more secular governments. That will not happen because the only one is Jewish. The only other thing is to be neutral in this whole sunni-shia divide. If they want to fight and kill over whether to follow the son-in-law or father-in-law of muhammad we cannot stop them but the US should not be a part of it. If that means giving some leeway to Iran I think we should do that instead of coming exclusively on the side of Sunni arabs.