BrotherMan, you have to be true to yourself. Mary has to be true to herself.
If you are truly poly-oriented (and only you can know this), and she truly cannot accept that aspect of who you are (and only she can know that), the choice becomes then, how much of yourself are you willing to repress for the sake of this relationship.
I cannot pretend to know what you should do, but I can say what I think I would do in that situation. I would take my broken heart and sadly walk away. I choose to be fully who I am, and I want my loved ones to be fully who they are, whether we are together or apart.
Whatever you decide, I wish both you and Mary the very best.