It's so much deeper than that. For a lot of these *phobias, the concept of being friends with such a person is so foreign that merely reading a story about inter-group friendship has a measurable positive impact. See the below excerpt.
Participants who read a story about the friendship between a member of a stigmatized group and the member of another outgroup scored higher on outgroup admiration than a control group and felt less threatened by the prospect of interacting with a member of the target outgroup. However, reduction of outgroup disgust, negative stereotypes, biased beliefs, and anxiety was or tended to be highest among participants who read a story about the friendship between a member of a stigmatized group and an ingroup member. (p. 747)
Basically, it's like these people have never imagined the target of their bias as someone who you COULD be friends with.