As the word states, "Islamophobia" implies an irrational fear of Muslims. Phobia means irrational fear.
The fear of Muslims being potential terrorists is not an irrational fear, but one that has developed over time. The fact people have been exposed to many acts of terror made by extremist Muslims (mainly by the media, of course) causes our brains to develop a fear of anything Muslim-related.
This has, of course, roots in our basic survival instinct. Our brain subconsciously starts to perceive Muslims as a threat as part of our innate instincts. This idea is not necessarily a bad thing per se (it's a quite normal development), but it can (and does) lead to bigotry, with different levels of gravity varying per individual.
All this said, I'd rather not blame Islam itself, but any kind of extremist or fundamentalist ideal that leads to violence and intolerance, as well as the people that spread them and drag others into them. And in the conservative-progressive spectrum, a balance must be found as well. Extremist left is just as bad as extremist right.
Being too politically correct does lead to a kind of tyranny and suppression of free speech under a fear of others being offended by a wrong choice of words...
Thing is, people tend to become extremists under the presence of extremism. Either they adhere to an ideology or they try to fight it with an extremist opposite. I feel that is going to be a problem in our world for the coming years.
It's happened in the past and signs point towards it happening again. Like history is doomed to repeat itself no matter how hard some try to break the cycle. Above everything, everyone is just trying to survive their own way...