How to keep yourself composed in moments of distress or conflict?

I don't think there is one "magic pill", because situations strongly vary and if someone gives you a one sentence formula it will be too stiff to adapt to the different things you encounter.

I think it's better to focus on progress over perfection. After one interaction, enter in "scientist" mode and ask yourself "what happened?", "what could I have handled differently?". If you do that enough, you'll discover patterns in yourself and others (for example, "X always gives me the cold shoulder to make me jump"), and you learn and improve for the next time. Don't be hard on yourself, we all have areas of improvement and nobody can cover beforehand all the possibilities. Murphy exists...

Learn to control your anger. Learn not to react, but think about the subject. Many people, like yourself, get instinctively angry when it comes to certain topics. They will fly into an angry rage and the discussion ends up becoming one side attacking the other with personal attacks. It's an easy trap to fall into and many people don't have a handle on their emotions when it comes to debate or discussions.

The way you stop getting angry is to stop immediately reacting. Calmly think about what the other is saying. Try to see it as if your someone who has no personal stake in the outcome. And make a pledge to yourself and others than even if you raise your voice you will always be their friends and hold to that. No matter what the subject matter.

Take a deep breath and shut your mind down for just a few seconds before you open your mouth.

Deep breathing, the kind that fills your lungs completely and then letting the air out slowly, is shown to activate the parasympathetic nervous system which slows the heart rate, releases serotonin, and can help make it easier to control anger (which is a sympathetic nervous system and limbic system response).

Those are those moments when I have to walk away and say “I need some time to calm down, give me a minute please”