But then T met me and we became deeply involved, developing nothing like a "swinging" relationship and definitely more of a poly one. Once this happened, I requested a certain level of privacy. . . .
G, however, still feels she needs to read everything we discuss. It has gotten to the point that we no longer flirt or sext and keep everything very "business like". I resent it but when I brought my objection up with T, he told me "this is the way we've always done things."
Am I wrong to feel so....violated?
You said you requested that it no longer happen, and that G still "feels the need" to still read the texts. So, your request wasn't agreed to, T continued to allow the access, and you dialled back to "business like." I don't think you've been violated. Your initial privacy request was not agreed to (unless I missed something in the narrative), so you are respecting a personal boundary that protects your privacy.
Actually, I do have access to their home (garage code and key) and he does mine. I also have fingerprint access to his phone. He has the same. . . .
There is a lot about our relationship that mirrors a "primary one".
So, you consider it normal for a "primary" relationship to include access to each other's phones, but you expect that access not to be used for reading private text conversations? In a situation where reading text conversations has been a normal part of their dynamic? And you describe G as "extremely threatened by me and our relationship"?
With all this context, it sounds to me like you're asking a lot of G, and really setting her up to fail. Will you ever really trust her not to use her access to his phone to read the conversations? Would you expect T to revoke her access to his phone, when that, to him, is a special sign of closeness, and you and T have access to each other's phones?
If T and you share reciprocal phone access, and T and G share reciprocal phone access, I think you're best off just keeping your texts businesslike as you've done, and getting over the resentment.
If sexting privately is more important to you than sharing phone access, then make the gesture of revoking each other's unfettered access, before T revokes G's. Otherwise you're asking for a higher level of access than his wife has.
If you must have both access and privacy and want to see how far you can push the wife who already has a problem with you and your relationship with her husband ... well, play that game. But I don't think it'll make anyone happy in the end.