The Iran-Syria alliance has been in place since the Iraq-Iran war going back to the times of Hafez Al-Assad. They both have also been historical backers of Hezbollah.
While they were somewhat less close than they are today, they have long been sharing strategic interests.
Also Arab states lead by Saudi Arabia did in fact support the Syrian opposition, but only because they always seen it as a vehicle to replace the Alawites with a Sunni aligned Islamist government. Or are we going to pretend that Saudi Arabia is a friend and sponsor of secular democracies? And their support of the Syrian opposition doesn't mean they were actively doing anything against ISIS, on the contrary, most of the funding and arms funneled into Syria ended up with ISIS or Al Qaeda as Sunni opposition groups started attaching themselves to either to ISIS or Al Nusra.
In this very specific situation the narrative does in fact fit perfectly. Sunni influence in the region is cancerous and destabilizing while the Shia very much represent a less toxic and more stable side.
Sunni Islamism is exponentially more dangerous and toxic than Shia has ever been.