How do YOU deal with people who disagree with you?

I’ve been thinking lately about my childhood, and the way I was brought up.
The more I think about it, the more I see that a) my mom had no friends, and b) anyone who disagreed with her views was immediately excommunicated and in all other ways excised from our lives.
This was highlighted for me when, this year, my older brother got married, and my mom did not attend. They had gotten into a fight some months earlier about how our younger siblings were being raised, and have not spoken since.
As I thought it over, I realized that it in situations of extreme disagreement, I too, had been known to fall back to this paradigm. Since that realization, I have made a conscious effort to remain rational when involved in disagreements, and not simply pretend that the person does not exist anymore.
I am curious, how do other people deal with disagreements, significant or otherwise? How do you think the way you were raised, or behaviors you witnessed in childhood affect your choices in these types of situations?