Wordorigins.org

The Associated Press Stylebook, which is something of the standard setter among American journalists, has come out discouraging the use of the word homophobia (and Islamophobia as well):

phobia
An irrational, uncontrollable fear, often a form of mental illness. Examples: acrophobia, a fear of heights, and claustrophobia, a fear of being in small, enclosed spaces. Do not use in political or social contexts: homophobia, Islamophobia.