Last time it happened, the Saudis sided with Zaidi Imam Muhammad al-Badr.
It was the year 1962, when revolutionaries inspired by ideas of Arab nationalism deposed the last king of Mutawakilite Kingdom of Yemen, Muhammad al-Badr, and put an end to the rule of Zaidi Imams who had been kings of Yemen for the most part of past one thousand years.
Inspired by socialist ideals, Arab nationalism had emerged as a potent ideology around the Arab world and Yemen was no exception. Jamal Abdel Nasser, the then socialist Egyptian president, backed the republicans in Yemen through military support while Saudis, along with Britain, supported the deposed Zaidi king who spearheaded insurgency against the new government.
Not many people outside Yemen know about the Zaidi sect of Islam that exists in the southern part of Arabian Peninsula.
The Zaidiyyah, who are also known as 'Fivers', are named after Zaid ibn Ali, the grandson of Hussain ibn Ali. Zaidis follow the jurisprudence that is more similar to Hanafi school as compared to the 'Twelver' Shia school of jurisprudence.
Houthis, mostly Zaidis, started as a theological movement in 1992 and spearheaded insurgency in 2004 against the then president Ali Abdullah Saleh, who himself belongs to the Zaidi sect. The Houthis, along with students and Joint Meeting Parties, participated in 2011 Yemeni revolution that followed the Tunisian revolution.
In 1962, Zaidi Shias were friends while nationalists, socialists, and communists were pronounced as foes by the Kingdom of Saudi Arabia. In 2015, they have been declared as foes and an imminent danger to Saudi sovereignty and territorial integrity.
It is most convenient to paint the whole conflict with broad brushstrokes of Shia/Sunni and Arab/Ajam binaries while ignoring the role of imperial baggage, complex socio-political realities, and all-powerful ruling Arab dynasties.
Also see: Bad Saudi vibes