I'm a lesbian and I think that my roommate could be slightly homophobic. We have never really had a great relationship but now that I've come out to her, we don't talk much at all. How do I talk with her about this issue so that we can put it behind is without making it so awkward?
A lesbian and a homophobe surely add up to a tense roommate scene. But from the sounds of it, you're willing to tackle your small corner of homophobia in the world, for the betterment of your living situation and your roommate. Keeping on point in your conversations with her about your relationship, as well as asking yourself some questions before you talk to her to clarify your objectives will go a long way towards alleviating the awkwardness inherent in these difficult types of conversations.
A working definition for homophobia is the irrational fear and subsequent discrimination and/or hatred of non-heterosexual persons, including gay, lesbian, bisexual, transgendered, questioning, or queer people and sexual non-conformists. That being said, homophobia encompasses a wide range of viewpoints and attitudes, and manifests differently in different people. While there is no one known cause of homophobia, research has shown that having strong religious beliefs disapproving of sex and/or homosexuality and having little or no contact with lesbian and gay people can negatively influence a person's attitudes towards homosexuals. Homophobia affects everyone — when a particular group is marginalized or intimidated, no one can feel truly safe.
It's admirable that you want to address your roommate's behavior, and some good things may come out of these ensuing conversations. In these early discussions, try to approach the subject with compassion, giving her the benefit of the doubt. Steer the conversation so that arguing or fighting is avoided, especially about other issues besides the topic at hand. If she hasn't been introduced to the idea of homophobia, it could easily feel like an attack — be in control of the situation enough to state your feelings and concerns while keeping dogma and preaching out of the picture. While ignorance is no excuse to discriminate, the learning and change must have a beginning, hopefully in you.
It may be helpful to consider aspects of her life and circumstances before beginning your conversations: are you the first lesbian she's known? What were her experiences of lesbians and gay people before you met her? Articulating exactly how she displays homophobia will also be valuable to do before having a conversation. Does she give off a distinct coolness? Judgment? Unkind glances or comments? Check out some organizations dedicated to gay-straight alliances as you're addressing these preliminary questions. Gay, Lesbian, and Straight Education Network (GLSEN), Parents, Families, and Friends of Lesbians and Gays (PFLAG), and Human Rights Campaign (HRC) are some excellent places to start. Queer student organizations on campus may also be a good source of support, as it is likely someone will have encountered something similar before.
Also keep in mind that carrying the torch to end homophobia (so to speak) can be tricky. You are advocating both for her treatment of you and for wider understanding and tolerance of all queer folks. At the same time, it may be best to have reasonable expectations. For her, this may not be something she can "put behind her," but will resonate and bring up new issues. The light you're shedding on this subject will carry far into the future, and you may never know exactly what impact you've had on her thinking. Staying true to discussing how to successfully room together given your differences in sexuality may be the best point to hone in on.