Islamophobia just as homophobia even though it's intuitive to think its only about fear because of the phobia part in actually is about BOTH fear and hatred. Look up the definitions and you will see.
As far as Islam. well people that follow Islam are Muslims, and like all kinds of people they are NOT a monolith. So it's impossible to say all Muslims this, all Muslims that.
So people should not hate Muslim people just because they are Muslims.
You may learn stuff about individual Muslim people that logically makes them hateful in your eyes, but if so, it should be about that, not just that they are Muslim people.
A personal note. I'm not proud to say this but I've had a few experiences in life of short term relationships with Muslim people. They were openly Muslim and hearing about that part of their lives was interesting to me. One (Malaysian) was even a Hajj tour leader! Also a Thai Muslim who complained to me that f-rangs discriminated against him. However, I intentionally did not tell them I was a Jew because I was afraid they would hate me for that and I wanted them to see me as me without adding that complication. I didn't give them a chance to prove otherwise. They just assumed I was a non religious Christian, a fair guess. Obviously that would have had to come up in longer relationship.