That "condoms with others" rule is purely for protecting couple's privilege.
It CAN be used this way, but not always. My partners and I have this rule. They also know that it can be renegotiated on a partner-by-partner basis, after the relationship is well established and transparency, trust and ability to start hard conversations has been established.
I have a compromised immune system and certain STIs could be very dangerous to me, particularly HPV, which I’m too old to get vaccinated for, and Hep B because the vaccine doesn’t work on me. My ex has had several women lie to him about history, risk, and even say a condom wasn’t needed. If it’s not needed with him then they don’t use it with others.
He's had women refuse to get tested and worse, he has had partners who went to get tested have doctors say they’re fine and it's not needed. All shady shit. So yeah, all of my partners agreed to condoms with anyone until the above standards were met.
We have all experienced men say they can’t use them, or refuse and guilt women into going without, and women have been trained through patriarchy to please men, and that means not using condoms. You need to make sure the person you are with can enforce boundaries, say no, and use condoms without issue to truly know that they have the capacity to do what they can to reduce risk And have the hard conversations about that before sex and, if there happens to be possible exposure, have the ability to have hard conversations afterwards about either not using a condom (it happens) or possibly being exposed (if a partner comes up positive for something or is having symptoms).
For me, it’s not about specialness or punishment. It’s about informed consent. I cannot give informed consent if anyone in the polycule is choosing to be dishonest.
They also know they can choose not to abide by this agreement. At that point they would have to use condoms with me instead, which I have no issues with.