Ok, to be super honest with you...I really don't think you're in a good spot to be that upset with this right now.

First of all, you kept and keep complaining and worrying about her spending time with men who are gay(if they say they're gay, that's what they are) but in the meantime you cheated on her. You're not necessarily a bad person for cheating but you did break the trust, you broke the "terms" so to speak.

Secondly, you aren't happy with her not wanting you to be around other straight women and you think it's not fair but you actually did cheat, you proved her worries right.

Thirdly, in my opinion you're both having serious trust issues and are somewhat immature in this relationship. Others may disagree, we'll see, but my opinion is that people of all genders and sexual orientations can in fact be just friends with each other. Think about it, do bisexual/pan people have zero platonic friends just because they are attracted to members of any and all genders? No, right? It's the same with straight people, you aren't automatically attracted to everyone around you, even people you find attractive to look at, just thinking someone looks attractive doesn't mean you will feel anything more.
But the biggest issue here is that there's zero trust between you. Hers turns out to be justified, yours probably isn't and tbh it really doesn't matter.

Truth is that this policing of who your partner can hang out with and obsessively following what they're doing all the time, is a sign of deep mistrust and insecurity and it doesn't actually do anything good. Think about it, she doesn't want you to hang out with straight female friends and yet you still managed to cheat. If your partner wants to cheat on you, they will, no matter what "rules" you have in your relationship, no matter how much you both try to always know what the other is doing.

Also, I think it's worth saying that if you feel the only way someone won't cheat on you is if you are setting rules and always checking up on their every move and so on, they may as well cheat because what should keep someone from cheating should just be that they really don't feel like being with anyone else, choosing not to themselves.

I am saying these things not to point fingers but because I think there's a lot of things that you might both want to discuss about your relationship in general and everything, see how things really stand because this right now doesn't sound like something very good for either of you. Also, you might want to think hard and deep (and be honest with yourself while doing it), on why you cheated and what that might say about your feelings for your girlfriend and the all around satisfaction you get from the relationship.