I'm kind of torn... On one hand, I think requesting that a partner use barriers with others is perfectly reasonable to maintain fluid bonding. On the other, since she entered the situation with you ALREADY going barrier free with this other couple, it seems odd that it's just now bothering her.
I would talk to her more. Find out where her motivation is coming from. Is it an STD concern? Or is it a control issue/wanting to seem more important? Is it something she wants you to do forever or something she would appreciate you doing until she is nearby and can meet these other people to become more comfortable with them?
Considering she's a mono person, I think it's a bit harsh to judge her too much without getting to the root of the WHY. She's working on completely changing her views on relationships to make this work, no point in making it any more difficult than it already is if it's something fairly simple to do.
Personally, I hate condoms. Boy and I go back and forth between using them and not, depending on what other sexual connections he has at the time/testing/etc. I have no problem whatsoever telling him that I'm dating someone new, that person is uncomfortable with me going bareback with someone who I don't have many agreements with, therefore we're using condoms again. Hubby and I have multiple agreements in place about who we do/don't have to use barriers with, what activities are okay with/without barriers, how often we get tested, and all that jazz. I would NOT be willing to use condoms with him because I know he takes all the precautions that I feel are necessary to keep us as safe as possible (without being a complete buzzkill).
I guess, I think it's a matter of priorities. Yeah, it sucks to be fluid bonding and then go back to barriers, but I personally think it's worth it for some people. And I have never once had someone complain when I've decided that barriers are needed again for whatever reason (be it my own personal thoughts or someone else's that I decide to respect). What's more important? Maintaining fluid bonding with this couple or respecting your partner's feelings on the matter?