Indeed. I am certainly not an expert, but it seems clear that the situation is much more common than a simple Sunni/Shi'a issue, although the western media has a tendency to frame it that way to fit it into the narrative which they use to simplify the entire Middle East conflagration. The situation seems to be extremely complex, with many factions and shifting alliances. Now, of course, this is all further complicated by the Sunni-led coalition which has been bombing the country for the past two nights.
Given all this, I really doubt there is a monarchist solution (or really, any viable solution) in the near or medium term.