All of the online dictionaries at onelook.com list homophobic as an adjective and none list it as a noun.
As the poster notes, there is an accepted noun for a homophobic person, homophobe.
As Mr. Shiny and New notes, adjectives are often used as nouns. However, in most cases, this is limited to a collective or categorical usage as in his examples, such as the fast and the furious. You can say the race goes to the swift, but you cannot say the race goes to a swift (unless you are talking about the bird).
As @WS2 points out, adjectives are often used as nouns to refer to someone who has a condition, such as a diabetic. This type of usage can refer to individuals or a whole category, and can take a definite or indefinite article. These seem to be limited to cases where there is not a separate accepted noun for the thing that has the adjective's quality.