What is the best way to communicate your frustration with someone without them flying off the handle because you have feelings they disagree with?
Put it in writing. The cannot interrupt and can take the time they need to process what you have to say. Just hand them a letter, and walk away. When they are ready they will respond.
Dear Hope Hunter,
Here is another thought for your consideration, in addition to the ones you have already received:
If the person is disagreeing with you so much that they might fly off the handle, perhaps it is time to give that friendship/relationship a break. Over time you will come to know if the break is only temporary or perhaps permanent.