Nibras Kazimi, who blogs at Talisman's Gate, has a long essay out for the Hudson Institute that you ought to read. It's focus is on the ideological contest being waged between Saudi Arabia and ISIS over who can claim to be the true defender of the Sunni faith in the face of Shi'a aggression. To give you a taste of his arguments:
The jihadists of the Islamic State have had a lot to say about the Kingdom of Saudi Arabia. They do so because they see themselves locked in a rivalry with it. At the heart of the rivalry is the question of who gets to pose as the defender of ‘Sunnidom’ in the face of Iranian expansionism in the Middle East, a perception both rivals share and agitate over. The Islamic State argued that the House of Saud has lost the legitimacy and efficacy necessary to mount such a civilizational defense. They cited the static nature of Saudi inaction, one that did not correspond to the alarmist rhetoric emanating from Riyadh concerning Shi’a transgressions against Sunnis. The jihadists may believe that this disconnect between rhetoric and action is accelerating the disaffection of Saudi citizens with their rulers. They may hope that this disaffection would welcome the expansion of the Islamic State into the Saudi heartland—a goal that is critical to the long-term survival of their state, or so they may believe.
However, Saudi Arabia’s regional policy is no longer static. A year ago, the Saudi state launched a military operation in Yemen against rebels it deemed beholden to Iran. The jihadists responded with disdain and mockery. They assumed that it was a fluke occurrence and that the war would expose Saudi feebleness and irresolution. Yet in December 2015, the Saudi state went further and declared the formation of an Islamic military alliance to combat terrorism. The implication was that Saudi Arabia is willing to take the battle to the jihadists in Syria and elsewhere. The move was also widely interpreted by Middle Eastern observers in media and intelligence circles as one that seeks to counterbalance Iranian activism across the Middle East. One Saudi-focused analyst wondered whether it constitutes the formation of an Islamic equivalent to the North Atlantic Treaty Organization (NATO). This latter perception has seeped into the public debate across the region, raising expectations of a “new order.”
The jihadists were not prepared to consider the possibility of such an unprecedented paradigm shift in Saudi behavior when they first analyzed the Yemen campaign. Their anti-Saudi narrative was tailored to address and belittle Saudi inaction, and now it must play catch up to Saudi action. They must also address the ideological ramifications of the kingdom positioning itself as a “warrior state,” harking back to a centuries-old identity that it used to manifest prior to its founding in 1932. The rhetorical arsenal that the jihadists had developed and deployed in previous years is ideologically insufficient to counter a rival warrior state, especially if it is Saudi Arabia. Now they will have to contend with the possibility that Saudi Arabia’s new expansionist policies may be well-received by its citizens, whom the jihadists were hoping to recruit and incorporate into their own expansionist state. The jihadists must now argue that Saudi action is illegitimate. That is a harder argument to make compared with one centered on Saudi torpor since the Saudis are doing precisely what jihadists for years have criticized the Saudis for not doing. It is especially harder should Saudi action lead to a radical rearrangement in the balance of power in the Middle East. As such, ideology follows action, and the jihadists were caught by surprise, at least for now. But the Islamic State could possibly find its footing if or when the Saudi-led Islamic Alliance fumbles on the terrain of battle or even if it fails to launch at all and falls short of meeting the expectations it has raised. Saudi Arabia may have felt compelled to take such a gamble, given what the jihadists were saying about its inactivity and other internal socioeconomic and cultural challenges at play. But it is a dangerous gamble nonetheless. If the Islamic Alliance ends up perceived by Saudi citizens to be a failure, then that perception may accelerate the loss of the regime’s cache of legitimacy. The jihadists may then spot an opportunity to gain ground within the kingdom, directing more of their personnel, resources, and propagandist attention toward that goal. (emphasis added) 
I strongly recommend you read the entire thing. Kazimi takes a deep dive into the propaganda used by ISIS, the official speeches and statements of the ISIS 'caliph' Abu Bakr al-Baghdadi, and the way Saudi policies (especially the new Saudi-led alliance) are being described by people in Saudi Arabia itself.
I cannot add much to Kazimi's analysis of these sources. However, his essay illustrates a point too often forgotten in most Western analysis of Middle Eastern affairs that is worth reiterating here:
International politics is not all about America. This is an idea most agree with in the abstract but inevitably fail to recognize in the moment. What Kazimi describes as a "paradigm shift in Saudi foreign policy" has been observed by many, but ISIS is rarely given much credit for it. Observers almost always focus their attention on the regional rivalry between Riyadh and Tehran, suggesting that the Saudi led Gulf Cooperation Council has been ramping up their efforts to contain Iran's growing power because of the United States' decision to slowly detangle itself from the region. In this version of events, a strong American presence in the Middle East is all that is stopping the escalation of regional tensions.
Kazimi's essay is a refreshing critique of this argument. In his telling the catalyst for Saudi expansionism is not fear of Iranian military power, but fear of salafist-jihadi ideological power. The Islamic State is an existential threat to the house of Saud; its very existence puts the legitimacy of their kingdom to question. ISIS critiques have revolved around the Saudi's inability or unwillingness to protect Sunni populations from the bullets of their enemies.The kingdom's new foreign policy is designed to put all such questions to rest. Saudi Arabia will be a warrior kingdom, and against such a kingdom ISIS's ideological assaults have far less power.
The point I would like to drive home here is that this likely would have happened regardless of changes in Persian ambitions or American force structure. The audience for Saudi action abroad is first their current subjects, and second other Sunni Arab populations across the region. In taking the fight to Yemen, by building a new "Islamic alliance," and so forth, the Saudis are responding just as much to threat posed by ISIS as to the threat posed by Iran. That threat would be a present danger to the Saudi regime regardless of American intentions towards Iran or the region as a whole.
OTHER SCHOLAR'S STAGE POSTS ON THE WAR FOR ISLAMIC CIVILIZATION
The Fight Against ISIS: Some (Unorthodox) Points For Discussion
T. Greer. The Scholar's Stage. 17 November 2015.
Iran: The Debate We Should Be Having
T. Greer. The Scholar's Stage. 24 July 2015.
A Civilization Is At Stake Here
T. Greer. The Scholar's Stage. 21 February 2015.
 Nibras Kazimi, "Saudi Arabia's 'Islamic Alliance': Major Challenge for Al-Baghdadi's Islamic State, or Potential Opportunity," Hudson Institute, white paper, March 9, 2016.