Although Command & Conquer: Generals made no explicit references to religion, it appears that the Global Liberation Army is based on Islamic extremist organizations such as Al Qaeda and the Taliban. Its vaguely Middle Eastern architecture, guerrilla warfare, tunnels, suicide units, accents and lines ("The higher order shall reign!", "I move to a sacred place!", "Infidels!", etc.), and use of anthrax and stolen nuclear weaponry are all evocative of radical Muslim terrorist groups that dominated the zeistgeist of the early to mid-2000's. In fact, when the Islamic State of Iraq and the Levant rose into prominence in Syria 10 years after Generals' release, fans of the game were quick to draw comparisons between ISIS and the GLA.
As of the Rise of the Reds timeline, the GLA is currently based in Central Africa, below the Sahel line that divides the Muslim and Christian parts of the continent. This means that aside from the original GLA veterans who have relocated to Africa, much of the GLA (the native African recruits) are largely Christians, animists, and syncretists. This is verified by the December 6, 2013 update, which states that Sulaymaan's Mercenaries engage to traditional rituals before battle. However, even the RoTR universe hints to the Islamic fundamentalist nature of the original GLA: Both Mohmar and Sulaymaan wanted to form a new anti-Western caliphate, and Yusuuf was originally the head of a Saudi fundamentalist cell with ties to Al-Qaeda.
Though religion is always a contentious subject to discuss, this is a measured and balanced attempt to explain the spiritual aspect of the GLA. Hopefully, resolving this issue will enrich the lore of Rise of the Reds.
First of all, it is important to note that not all "Islamist" militant groups are the same. Considering Mohmar's Kazakh heritage, he is assumed to be of a Sunni background. There are roughly three ideological tiers of Sunni Islamist groups in terms of roots and goals.
1. Generic Sunni Islamist
Your run-of-the-mill Islamist militants seek to establish Sharia into the political system. They do not necessarily aim for the reestablishment of the caliphate, however, and they are willing to form alliances with secular and Shi'ite groups. Sunni Islamist organizations include Hamas, Algeria's Islamic Salvation Front, and the Moro Islamic Liberation Front. The Muslim Brotherhood also belongs in this category, but it publicly eschews violence.
2. Salafi
Salafism is a movement within Sunni Islam that sees the 7th century as the pinnacle of Islam and all subsequent innovations as blasphemy. Though most Salafists reject violence and even disavow any form of political involvement, some Salafists believe that violent jihad is justified in "purifying" Islam and reestablishing the caliphate. Salafist groups like Al-Qaeda and al-Nusra Front are particularly hostile towards Shi'ites and Western influences. The Taliban may also belong on this category, though its philosophy lies in Deobandism and Pashtunwali.
3. Takfiri
Takfiris go beyond Salafi jihad and see all non-takfiri Muslims as apostates. ISIS, the leading power of the takfiri movement, has gone as far as to declare itself the caliphate outright, and claims spiritual and temporal jurisdiction over all Muslims. Once the Syrian branch of Al-Qaeda, ISIS now competes with its former parent organization over influence in the global jihad network. Other takfiri groups include Abu Sayyaf, Boko Haram, and the Caucasus Emirate.
Although Mohmar's original militia group may have opposed the secular Kazakh government on religious as well as on other grounds, a man with lofty goals of ridding the world of Western hegemony must have realized that basing his army on ideological puritanism would ultimately limit its expansion. He therefore formed the Global Liberation Army as an umbrella group, uniting Sunnis and Shi'ites under a common goal of driving Western influences out of the Muslim world. This explains how the GLA managed to receive funding from Shi'ite Iran while also joining forces with the Sunni Brotherhood of the White Falcon.
Hamas and Hezbollah would have joined the GLA due to their common anti-Zionism, while ISIS and other takfiri groups would have been brutally crushed and their ranks and resources absorbed. The latter action may have given the GLA a measure of support from those weary of ISIS violence, even though Mohmar may have personally seen al-Baghdadi as a role model in terms of brutality and exploitation of social media, if not religious dogma. Meanwhile, former ISIS members and Yusuuf's White Falcon Cell would have provided a source for the GLA's suicide bombers and a means for international recruitment.
Of course, there is a flaw to the Mohmar's umbrella strategy. Elements within the GLA have been known to defect on a whim, as demonstrated by China and Prince Kassad, and in the absence of a strong leader, the entire organization collapses altogether, with splinter cells more content on fighting each other than fighting Western oppression. Sulaymaan managed to reunite the GLA only through his skills in manipulation and utter cruelty, possibly developed from his experiences with ISIS.
Fast forward in time, the GLA is forced to retreat southward as the ECA flushes it out of its base in North Africa. Regrouping in the proverbial Heart of Darkness, the GLA had to adapt its umbrella strategy to the religious and ethnic mosaic of Central Africa. It from then on became a largely secular entity, whose ranks include Sunnis, Shi'ites, Christians, animists, and syncretists who blend any or even all of the four. Himself a Sunni Muslim with ambitions of becoming caliph, Sulaymaan nonetheless downplays the Islamic roots of the GLA , lest he alienates his non-Muslim subjects and allies. In turn, Yusuuf and his White Falcon cell are given free rein to proselytize their brand of fundamentalist Islam among the native population as well as on the Internet, providing a steady source of suicide bombers and kamikaze pilots for the Cause. Foreign missionaries and religious charities are barred from entering GLA territory, ensuring that Yusuuf's apostles face no competition.
In conclusion, the Global Liberation Army was neither Islamist nor secular. Though it did not espouse a secular ideology, it set itself apart from its terrorist predecessors by uniting disparate, even mutually hostile groups under a common mission of defeating Western imperialism in the Muslim world. As its influence expanded across the globe, the GLA turned to nationalism and class conflict to draw support from non-Muslims. By the time it reemerged in Central Africa, the contemporary GLA has become a truly secular entity, a "warrior paradise" where the dispossessed and the discontented from all over the globe make their pilgrimage to exact vengeance upon the world.