Well, personally, I don't see fluid bonding as something you only do with romantic partners. For me, it is to do with convenience and a level of trust that I could have with a friend. The trust you need in someone to minimise the risk of Std transmission isn't only something that can be achieved in friendships, I think it's unwise to think that every primary style partner you have is automatically fluid bonding material. For me it depends on the person, the relationships they are currently in, their status in regards to some life long Stds, the other relationships they are in and their general view on Std prevention. It seems your girlfriend is trying to keep something that is only shared between the two of you out of insecurity and fear.
I know it could be that fluid bonding with someone who is fluid bonded with others is beyond her acceptable level of risk, regardless of what safer sex practices these other people have. I doubt that though. Especially as it seems she is already ditching the use of barrier protection with you. It really seems more about the threat she sees them having to your relationship and wanting to keep something exclusive. The fact that you're long distance may contribute to get insecurity amongst other things.
It would be more reasonable for her to say "I'm not comfortable fluid bonding with you whilst you are not using condoms with other people. Therefore, we will continue to use barriers." That way, you have the choice whether to respect her boundaries and always use condoms with her, or respect her boundaries and always use condoms with other people.
If she wants to fluid bond with you, instead of trying to stop you from going bareback with this couple, she should think about what she needs to feel physically safe shunning the use of condoms with you whilst you are also having barrier free sex with them. This mainly revolves around testing practices.
She needs to understand that although she may see fluid bonding as an act of intimacy that is only found in primary style relationships, you might not and applying your value systems to your partner's relationships is rarely a good idea. I'm guilty of doing that, myself.
(Although I was right!)