People have a right to be afraid of any terrorists, but they are wrong to be linking every Muslim person with terrorism and if they do it becomes discrimination. They are painting Islam with a broad brush, when the real problem is those extremists and fundamentalists who exist in any faith.
I think people who are islamophobic are either discriminating based on the religion or that they simply just are not well enough educated about it. Islam does get a lot of negative press, especially from certain news outlets, and if you are not educated in what it really is then you might be scared. You just need to inform yourself.
Words like "Islamophobia" are coined right out of the Marxist-Leninist play book, to create an emotively loaded, but essentially meaningless term, that can be used to beat up others and force them into line. A phobia is an irrational fear. Most people disdain Islam for reasons that are not irrational fears. One only has to look at what becomes of societies in which Islam is in the ascendancy to see its failings, and to project the likely outcome into their own societies, if it is allowed to flourish. The other false premise here is that discrimination is a bad thing. Discrimination is a process by which one selects the desirable over the undesirable, and is an essential process that we all need to learn to use effectively. If a person chooses one way of thinking over another, it tells about their person, and indicates their suitability for all kinds of things, from work to relationships. Adherence to Islam tells enough about a person that the proper application of discrimination would mean selecting against them for certain things. But that does not just apply to Islam. For instance, I have an acquaintance, who is an employer, who would set aside any applications he received that were obviously from Jews or Muslims. He runs a system of pig farms and pork rendering plants.
I think there are two types of people who fear or discriminate against Islamic people. There are the racists who fear and discriminate because they are often dark skinned and because they are largely racist against all darker skinned people. There is also a group of Christians and atheists who discriminate against Islam because they fear the religion. While there are some people who use Islam to justify horrible things, the same could be said about Christianity. Also, just because someone is religious, doesn't mean that they will use it to justify bad things. I think the issue is too complicated to say it is always racial or always religious discrimination.
Being of afraid of Islam is not the same as discriminating against it. While I think those who "suffer" from "Islamaphobia" need to find a way to open their minds and get over their fears, I don't think it's religious discrimination to be afraid. I think the media and a lot of politicians actually send messages that make people afraid of Islam, and thus it's not entirely surprising to become that way. That said, unless the person is trying to abuse or infringe on the rights of those who practice Islam, it's not discrimination. It's a shame, but not discriminating.
Islamophobia is not better classified as religious discrimination. Islamophobia is based upon fear of Muslim extremism, namely murder and maiming. While people of all faiths can commit these crimes, the United States' experience with 9/11 really changed citizens' fear levels as it pertains to Muslims. Mainstream Muslims are not a problem with Islamophobia, just the extremists.