The answer depends on what level of analysis you choose to pursue. In a crude first analysis, we are opposed to Assad because the Syrian government is allied with our enemies, Russia and Iran. Similarly, we helped overthrow the Qaddafi regime in Libya because it was historically adversarial to the West; in contrast, we were lukewarm at best to the protests against Mubarak, and eagerly embraced the counter-revolution against Morsy. If Sisi is able to retain control of Egypt in the long term, we will surely remain close allies with his government, just as we were to Mubarak's.
In that sense, the question of religious fundamentalism is beside the point. We do not especially care about the ideology of the non-state actors; we support governments which are our allies and oppose those which are our enemies (or are allied with our enemies). But a closer examination of our allies shows the connection of our foreign policy to Salafism and reveals the primary contradiction that has created this decades-long war that the West cannot win.
The governments that are supported by the West are not generally "governments" as we understand them in our own countries. They are more like rigidly hierarchical organized criminal enterprises. That's true of the governments we have installed in Afghanistan and Iraq, but it's also been true all over the world for many decades. It was the case in Iran, Indonesia, and the Philippines during the Pahlavi, Suharto, and Marcos years; it is true in Nigeria; it was true in the Latin American dictatorships and is true now in Honduras; it is true in Egypt. Ultimately, the United States wants two things: it wants access to the economic resources of poor countries and it wants to control their foreign policies. These objectives are broadly inimical to the interests of the residents of those countries, so regular democracy will never produce governments that the United States can work with. Instead, we are obliged to supply financial and military support to comprador criminals who run their countries on our behalf.
The local criminals' side of the bargain is that they are enabled by Western finance to loot their own countries with impunity. From top to bottom, government administration in these countries consists of the opportunistic extraction of rents in the form of bribery. At the lowest level, people are forced to bribe the police, the department of sanitation, the property tax collectors, etc. in order to either free themselves from harassment or to receive basic government services. And at every level from bottom to top, bribes are kicked up the chain of command until they reach the ministers of oil, state, defense, and of course the family of the president. So Africa's only female billionaire is the daughter of Jose Eduardo dos Santos; the Karzai family absconds to the West to enjoy their looted fortune; the Shah's family is still rich thirty seven years after they were exiled.
To say that this situation is resented would be quite an understatement. The Taliban has popular support (and is going to win the civil war) precisely because it abolished the corrupt system of foreign obeisance and rampant looting. The Islamic State in Iraq exists for the exact same reason, and so does Boko Haram. In decades past these revolutionaries might have been Communists (in some places, like the Naxal insurgency, they still are), but Communism was defeated by the West 25 years ago, and Salafism is an adequate ideological successor in Sunni areas. It is a mistake to ascribe Salafism to religious schools sponsored by the Saudi government, although they have possibly contributed to the unifying message of the ideology. Salafist insurgent groups are as opposed to the Saudi monarchy as they are to the other corrupt looters, and Saudi Arabia is now doing a delicate dance with the Islamic State which I doubt they can maintain. On the one hand, the Saudis are inclined to support IS in its fight against Iran. But on the other, Salafist insurgency is the single greatest existential threat to the regime. I expect that the Salafists will continue to win.
Remember that 20 years ago, al-Qaeda was like, 50 guys camping out in Sudan and dreaming big. Today there is a Sunni caliphate in the Levant with a standing army and mechanized infantry. The United States cannot win this war, but we also will never stop fighting it until we are firmly defeated, as we were in Vietnam (and as the Soviets were in Afghanistan, where they played the same role that we do today).
