Unfortunately in my experience those that are anti-Catholic would never have a calm conversation or even listen to me or my dh. For those we knew who would have the hardest time with our conversion, we sent a letter. We knew there would be anger and wanted to give them all a chance to know our plans without a chance to immediately speak to us so that they could talk to us calmly. We did still get one very, very harsh email and one letter that wasn't as harsh but not open to up either. We lost relationships that I had had my whole life.
I still miss them. Other relationships, within and without of the family, changed greatly. After 6 years those relationships have still not regained what we once had.
On the positive side, a couple of people that had listened to me struggle through those couple of years of study and decision are now Catholic or waiting on paperwork to become Catholic.
I'd do it all over again. I've thought and thought if there was a different way that we could have shared the news of our journey and conversion, but I don't know what we could have done differently to get different results. During our journey we did ask these people to help us combat what we were learning. How we wanted a way out of becoming Catholic! Yet, none of them would help us beyond repeating the same anti-Catholic "facts" that were untrue. We received, during our study, a copy of The Trail of the Blood
and a Jack Chick book. From the pastor we received an email encouraging us to read through Romans verse by verse. I guess he thought if we did so we'd automatically see how wrong the Catholic Church is. We followed his advice, but the results were not as he had hoped.
I do not mean to discourage you. I hope that your experience will be much different! My advice would be, do not discuss unless everyone is calm and everyone is willing to sincerely listen to each other. If they have an anti-Catholic wall already built that may take some time before they are willing to listen versus lecture you.
Pray, pray, pray, pray, pray, pray, pray.....................................................