I'm reading an account of St. Francis of Assisi (English) which describes the first evangelistic efforts of his little group of monks as utter failures. They were ridiculed, persecuted, and misunderstood without any apparent conversions to encourage them in their efforts in those first couple years. Yet Francis saw the importance of simply living as Jesus did regardless of the visible outcome. He focused only on the process, not the product. Obviously his choices eventually impacted the world in ways even he could not foresee.
As difficult as it is to serve, love, tolerate and please the people around us, we do so anyway because we are imitating the Lord. It's not about whether we are right and others are wrong. It's not even about convincing or converting them to what the Lord wants of them. It's about doing what the Lord wants of us and leaving the outcome in His hands. If it's not a matter of serious sin for which we are obligated to openly disagree with that person, then we can demonstrate our love by leaving our convictions and preferences in the background to their choices. Even when we know that we are right and they are wrong.