Er, what ARE the "three types of Muslim sects that exist"? Sunni / Shi'a makes sense, and these can be subdivided into various juridical schools, philosophical traditions, lineages of authority, and Sufi orders.
Why would people be opposed to Islam? Well it's easy, if you belong to one of the groups whose interests traditionally opposes those of institutionalized Islam: Jews, Christians, Zoroastrians, Hindus, Sikhs, Druze, animists, or secular / irreligious liberals.
Islam, you'll notice, is implicated in various violent movements around the world (though some of these may be justified, and not all Muslims will agree with every jihad). More than that, various forms of Islam are significant political and social forces with serious implications for how people live their lives. Ever read Atwood's "Handmaid's Tale"? That was about super-weird fundamentalist Christians taking over America, but for Muslim societies, it's not so far off. Yes, there are liberal Muslims too, but the terms of the debate shift in strange directions.