I think the impact of the West works on three different levels. First, there is the basic effect of Western
realpolitik going back over a century, which has often led the West to support various strains of Islamic conservatism and Islamism (mostly Wahhabism in Saudi Arabia and less often the Muslim Brotherhood in various other contexts) in order to counter the Ottoman Empire, the Soviet Union, Arab nationalism, and today Iran. That is unhelpful at best, and treacherous at worst, given these movements' attitudes toward the West. It is something Middle Eastern secularists and religious minorities will find very hard to forgive the West for.
Second, there are the specific violent actions the West has conducted and/or supported in the Islamic world. In cases like Iraq and Libya, they've helped open up the space the jihadis require in order to operate. But more than that, such violence can and does play a role in driving individuals to seek revenge. There's no point denying it - the jihadis regularly tell us that they act, at least in part, in response to Western actions in the Muslim world. It is a regular feature of individual martyrdom video explanations, and a large part of al Qaeda and ISIS propaganda is dedicated to highlighting the suffering of Muslims at the hands of Western bombs or Western-backed regimes. This doesn't necessarily mean that any particular Western action is inherently wrong - bin Laden for example got famously upset over support for the independence of East Timor and South Sudan at the expense of the Muslim countries Indonesia and Sudan respectively; but specific actions can and do play the role that, say, Bloody Sunday did in Northern Ireland in helping to drive recruitment for the IRA. And so logically a less heavy Western footprint in the region should go
some way to lessening the number of recruits.
However, where things get a bit hazy from there is when we consider the
other things al Qaeda and ISIS tell us about their motivations, and the
other actions they conduct - and this is where the role of Islam comes in IMO. Because the jihadis also regularly tell us that they're fighting to (re)establish God's law on earth; to restore the Caliphate; to reconquer Palestine, Spain, India, and all the other historically 'Muslim' regions lost over the centuries; to subjugate the non-Muslim world; to eradicate polytheism (hence the genocidal campaigns directed at the Yazidis - try explaining that one by referring to Western policy - and the Shi'a); and on and on. This is a body of ideas that almost all Sunni Islamist movements going back a century or more adhere to to some degree - where they tend to differ is over the legitimacy of the means used to achieve them, and the role of violence therein (The jihadis of al Qaeda and ISIS tend to combine the social conservatism and harsh sectarian outlook of Saudi-style Salafism (Wahhabism) with the revolutionary violence and fascist-like political program of the Muslim Brotherhood, or at least that wing of Islamist thought inspired by thinkers like
Mawdudi and
Qutb).
So what you have is a fairly coherent ideology whose main body of ideas and goals is derived from a particular understanding of the way Islamic history has played out over the last 200 years or so. And here we see the impact of the third level of Western involvement. Because it is from around 200-250 years ago that the Islamic world began to come under the domination of Western or Christian countries - Russia in the Crimea, Caucasus and Central Asia, Britain in the Indian subcontinent, the Dutch in the East Indies, and the French in North Africa. And finally, the British and French in the Middle East. For the Islamists, and probably for many apolitical Muslims, this is a betrayal of the way history was supposed to play out, and indeed had (in their eyes) played out up until that point - Islam was supposed to dominate the rest, not the other way around. And so the one thing that all Islamist movements - whether Sunni or Shi'i, jihadi or non-violent - agree on is that the Muslims must take control of their own destiny by ousting the West from Muslim lands and revealing it for the Paper Tiger they believe it is.
But maybe more than the military and political domination, and the economic domination that went with it, Islamist ideology has grown as a response to the effects of Western
cultural prestige and influence in the Islamic world - the fear that Muslims will forget who they are and what it is that makes them Muslim in the face of the spread of liberalism, democracy, etc; that they will become 'Muslim' the way that most Westerners today are 'Christian'. There's nothing unique to the Islamic world in this - retaining an authentic sense of identity has been a challenge for
all those regions that came under modern Western domination, including within the West itself. And it has helped provoke the rise of ideologies such as Hindutva, Fascism, Russian Nationalism, "Asian Values", etc. All these of course have their own unique points of reference which have shaped them and which they believe are culturally authentic - the role of Islam has been to shape these reference points in the
Muslim response to the West over the past two hundred years or so. Hence the focus of Islamist movements on things like
jihad,
shari'ah, and
Khilafa, all terms and ideas which carry huge weight for any Muslim with a conscious attachment to Islam. For any Muslim who feels that the modern world has been an unrewarding, harsh, and alienating environment in which to be a Muslim (and let's face it, there are good reasons why huge numbers of Muslims might feel that way), such ideas are likely to become rallying points in the attempt to change things for, as they see it, the better.