Iran is seeing its allies make gains in Yemen:
Saudi Arabia and the other Sunni states in Arabia see this as an Iranian attempt to form another Hezbollah in Yemen and do what the Hezbollah did in Lebanon. In both Yemen and Lebanon the Shia are about a third of the population, but because of the Iranian supported (since the 1980s) Hezbollah militia in Lebanon the Lebanese Shia basically have veto power over anything the Lebanese government tries to do. The Yemeni Saudis have made it clear that they will not tolerate this. This sort of Iran supported Shia takeover was always the biggest fear of the Saudis but it comes at a time when the Gulf Arabs and Iran are cooperating to fight a common enemy (ISIL). This is going to get messy and complicated. ISIL (al Qaeda in Iraq and Syria) is an immediate threat while, for Iran, Shia domination in Yemen is an opportunity.
Not that the Shias don't have grievances that even Sunnis admit are real and affect the Sunnis, too.
But don't forget Iran's strategic interest in Yemen and the Red Sea:
While we focus on the Strait of Hormuz, we could get blind-sided by an Iranian attempt to interdict the Red Sea and/or Suez Canal. Iran could lay mines in the Red Sea and increase the panic level in the West that could lead us to end a confrontation with Iran short of defeating Iran.
And having allies of Iran astride the Red Sea, from Hamas in the north through Sudan, Eritrea, and Yemen, could provide the access for Iran to attack the oil routes built to bypass the Persian Gulf close to Iran.