You always have the "right" to your feelings. Let me start by sharing that it is very normal to feel hurt, angry, betrayed, and disrespected when our partner cheats on us, even if it is with the same sex. It is important that you honor your feelings and then make decisions about your relationship. Can this be worked through? Sure, as long as you both are willing to talk and process through it. It really is up to you deciding if you want this relationship to continue or not.
If you do, it is a workable situation.