Loving yourself for who you are is an act of courage. Doing things that respect, honor and support those you love is also an act of courage. I understand that you see your situation as a dilemma. Do things one way, you are being nice to your parents and hurtful to those you love. Do things another way, and the reverse happens.
This dilemma comes from wanting to please those who judge you. If you let go of the desire to please those who judge you, the dilemma evaporates. What is judgement? In my opinion, those who judge me are saying who I am and how I live is bad and wrong. This doesn't have to be about polyamory. This could be about anything. This could be I'm bad because I eat the wrong kind of food, or live in the wrong city.
They are telling me to be someone else and live a different way so I can be good and right. Once I do all of that, they will be able to love me. This is nonsense. Does someone who tells me the real me is bad and wrong really love me at all?
In my opinion, you have two options:
The first option:
Let those who want to judge you do so at their leisure. That judgement will have an effect on their relationship with you. They will feel that effect. Let them feel it. It is of their own doing. That means they can undo it at anytime.
Allowing them to feel the effect their own judgement has on their relationship with you (instead of trying to do something different to please them so they approve of "who you are") is an act of love for yourself and those you truly love, because it prevents those who judge you from steering your life and the relationship you have with those you truly love.
I'm not saying you have to be unpleasant to them and tell them to get out of your life. I am saying live as you want to and let them judge you as they want to. There is no value in putting effort into trying to please people who judge you. Let go of your desire to turn off their judgements and put your energy into living your life.
Yes, it takes courage to do this. Love is an act of courage.
The second option is tell them nothing and live your life. The best choice is the option that brings you the most peace.