In the Sermon on the Mount, Jesus tells the crowd, “Love your enemies and pray for those who persecute you, so that you may be children of your God; for God makes the sun rise on the evil and on the good, and sends rain on the righteous and on the unrighteous.”
In my experience, there are two ways to fail at this kind of love for those who believe differently, two general categories: those who won't let the rain fall and those who won't let the sun rise.
I'm usually in the first category. My way of being around those who have different views is to just not bring up those differences. Avoid conflict. Or avoid them. Pretend that the sun is shining, or hold an umbrella over their heads so they don't feel the storm.
That's not Jesus' way of loving. He doesn't hold back from calling out injustice. He argues religious and political points vehemently. And far from avoiding his enemies, he goes out of his way to be around them.
He is most likely to step in when someone else is being harmed. When children are being shooed away or a woman is about to be stoned. He won't stay silent. But, he's also open to being changed by those he argues with, like the Canaanite woman.
Then there's the other category. Those who never let the sun rise on their enemies. Who refuse to see the humanity in them. Who don't care. Who can't forgive. Those who want to destroy their enemies.
That's not Jesus' way of loving either. He is always willing to receive someone from the opposition: a leader of the synagogue, a Pharisee, a centurion. Jesus has compassion for the rich young man even as he rejects Jesus' advice. He refuses violence in the face of arrest. He asks for forgiveness for those who kill him. He returns to the disciples who have denied and abandoned him.
How do we respond in love to those who have different views? Treat them the way we treat the people we already love. Get in fights when they do something to hurt us or when we see them hurting others. Defend our viewpoints, but also listen and be willing to change. (We might not be right as often as Jesus, either.) And also recognize our shared humanity. Have compassion. Find common ground. Forgive often.
I feel fairly confident that's the answer. It's just doing it that's so impossible.