If you pay attention to societal discord in America today, it seems at times like we are speaking 2 (or more) different languages. It is hard to communicate when you aren't speaking the same language or have different definitions of words.
One thing you can control is differentiating fact from opinion. It doesn't need to be said (I hope), but facts cannot be argued, opinions can be different.
When having a conversation with someone, especially a difficult conversation, be sure to use facts as often as possible and be aware of what is an opinion. This is one of the reasons during feedback we talk about observable behaviors - that are more facts. Whatever the impression is of the fact is usually an opinion.
If at any point during the conversation you notice that things are getting convoluted, take a step back and make sure you are differentiating between facts and fiction. Be sure the other person does the same. You'll find that when you agree on facts, then you can both agree that opinions are something that can be discussed without anyone being wrong.