"I can't figure out how these "families" think that the sin of someone else is somehow going to pervert the gathering. If that were the case, no one would have family gatherings ever!"
I can. I was cut off by my family (at my father's insistence) for the same sin-- but not because it was against God's will (my father recognizes no God but himself), but because it wasn't proper. What will the neighbors think? He claimed to be afraid that my behavior would lead the children astray, but I suspect that deep down, he was worried that the children would discover that the sinner was a kinder and better person than the righteous man.
Truth be told, though, it was a good thing. Without that separation from my family, I don't think that I would have ever found God. And, after I did, when I knew for sure that God was real and that Jesus died for my sins, my longtime sweetie and I got married. God has been sorting out my life and the lives of my beloved husband and children ever since. We are very blessed.
Sometimes I miss my mother, but she has done what she thinks was right, and biblical, and I don't fault her at all.
I think anyone seriously considering cutting off a family member in this way needs to be ABSOLUTELY CERTAIN that there isn't even the tiniest element of pride in the decision. Or any other sin. Pray hard on it. I can't say that it would never be the right thing to do, but asking God what to do is always the right thing to do first.