Saudi Arabia, along with the U.A.E., is at the forefront of the coalition of Arab states coordinating their approach to security. Their goal is to form a joint force of Sunni Arab countries to fight extremism in countries such as Yemen, Syria, Iraq and Libya. Wall Street Journal
Sunni Saudi Arabia is extremely anti-Shiite. Shiites constitute 10-15 percent of the Saudi population which poses a threat of rising against the Saudi Kingdom if Iran goes unchecked. If Iran goes unchecked the Saudi Kingdom could have Iran controlled countries to the north in Iraq and to the south in Yemen.
Iran is not strong enough to go against the Arab states in the coalition: Egypt, Turkey, Saudi Arabia, UAE… Iran will complain a lot about the bombing of Yemen but not spend many resources on the Houthis. Iran will continue to support Shiites in Iraq who they now lead and Hezbollah in Lebanon and Syria.
There is also concern that a wider Sunni-Shiite conflict could erupt with large foreign players involved (Russia), as well as fears that the chaos could embolden the terrorist groups already active in the region