Talking to people can often be difficult. You don't know what they think and/or how they feel. One second they can be calm, and the next they can come out of nowhere and verbally attack you. But there are ways to prepare yourself for the inevitable.
First, you need to realize that not everyone is going to like you. Not everyone is going to agree with you. Sometimes, people will get angry and make you feel like you're wrong. However, you both can be right in your own way.
People are free to form their own opinions and believe what they want to. You're not always going to agree with one another, but you ought to agree to disagree. Whatever personal bias you have can disappear for short period of time you're talking.
But when you feel an argument coming, remember your values. Stay true to who you are and don't change just because someone says something to try and break you down.
If you feel yourself getting heated, take a step back and take a breath. Open your ears and your mind. Don't make any preconceived notions or judgements.
Actively listen to their side and try to understand where they're coming from. Calmly voice your opinions as well as any suggestions you may have on how to resolve the issue.
To ensure the issue gets resolved efficiently, each party should come to a compromise and give a little. I know either side probably isn't backing down, but it's in everyone's best interest to give a little to get a little more.
It's hard to let go of pain and anger you've held on to for so long, but it will benefit society as a whole, I swear. Just live and let live.