What is Brandon's sexual orientation in Shame?

Does this imply he is a repressed homosexual that uses women because he is ashamed of himself, or that his addiction is so strong he even uses men to satisfy himself?

It was never clearly mentioned in the film itself but being familiar with the film I can surely say "his addiction is so strong he even uses men to satisfy himself".

He shows sigh of doing SMSM (Straight Men Who Have Sex with Men), it is a term mostly used in psychology study to differentiate homosexual from the guys who do sex with same gender even being straight. It can be done for experiment, after getting high or for being desperate enough for sex. For the case of Brandon he clearly show sigh of desperation for sex. He go from masturbating to sex to threesome so frequently to depict his sex addiction. And going to gay bar showed his sex addiction going to the limit of desperation to get sex. He never showed any attraction towards guy before this scene and had always shown open interest in having sex with girls all the time.

There are various article about SMSM on internet few are : joekort.com, glbtqarchive.com, straightguise.blogspot.in etc.

From joekort:

Men Who Have Sex with Men (MSM) is a term derived from the growing body of literature showing that not all men who have sex with men are gay. Adopted by sex researchers and AIDS organizations to classify men who have sexual relations with other men but whose sexual identity is neither gay nor bisexual, the acronym recognizes a reality that complicates our tendency to divide the world into heterosexuals and homosexuals, with a small number of bisexuals, who are sometimes thought of as simply gay men or lesbians who have not come to terms with their homosexuality. That is, the reality of sexual activity is more complicated than the traditional binary (or even trinary) system of nomenclature can accommodate.

They may have been sex workers or men who engaged in sexual relations with other men only because female partners were not available (as in the case of prisoners or men who live in all-male environments). They may have engaged in sexual activity with other men as runaway teenagers living on the streets for survival or as young men out on a lark.

Which clearly seems related to Brandon's case.

But if we really want to force him into a homosexuality category then he can easily be bisexual, bi-curious, pansexual etc etc but there is no support for it in film itself. I still don't support the theory of him being gay as he never showed any romantic or sexual attraction towards guys before that scene and only went to gay bar when he was not getting sex anywhere else. So I will still refer him to be indulging in SMSM.