I definitely think there is a chance that people would accept your relationship. I've been polyamorous with my fiance for almost five years now. At the moment we are also involved with two others. I've been upfront with my family from the start, and while they initially reacted badly, through honestly and communication they have become accepting of my choice and embrace having all my partners over for family functions. Lady, one of my other partners, has also been honest with her family from the start. They thought the lifestyle odd, but again respected her choice and also are happy with having all of us around for family time. My fiance on the other hand did not feel the need to tell his family about our lifestyle choice, although as we approach our wedding he has begun to let them know that we have a less than tradition relationship. They do not know the details, but they have seen how he has been happy through his years of relationship with me, and that is enough for them. Nova, my other partner, has faced a lot of controversy with his family because they are very traditional. They accepted he was in a poly relationship, but when they found out I was engaged they were upset because they saw it as violating the sanctity of marriage. They have since been both supportive and upset about it in turn. For example, his teenage brother is not allowed to spend any time around us because they believe the lifestyle is a bad influence, and they blame any relationship issues we have had on the poly lifestyle, even when they have had nothing to do with it. But they have also told him that he can make his own choices, and they are happy with whatever makes him happy. In regards to our family and community, some have expressed that they don't understand or agree with our lifestyle, but all have been supportive none-the-less.
Honestly, I think the real key in garnering the support of family and friends is based in being completely honest and upfront when it is appropriate, and by acting natural. If you act like it is okay to kiss your partners in public, or hold their hands, and everyone sees that you all are happy, very few will really feel that it is their place to interfere. If you are questioned about it, just be honest, it makes all of you happy and you all know what goes on and are content with it. While some people might speak against you for it, I believe in the long run that those who care about you will value your happiness more. Those who are not close to you have no right to speak against your private life to begin with, so act naturally with your partners and people will likely just act as though everything is okay as well.