Caring about people is a byproduct of knowing God's grace. I'm not giving up on anyone who is breathing air. That is my conviction
The number of people in the world is overwhelming. The number in our lives can seem that way. Needs go beyond us. We can only be in one place at a time. The beach is littered with starfish. We can only throw one back in at a time. Etc... etc...
Rest can live never giving up. It has the resources to live that way. Jesus sits in Heaven never giving up.
The next step after 'I'm never giving up' is 'I'll never be offended if rejected.' One enables the other. Try these two without the relaxation that grace brings and the fire will consume you. Jesus is fire that frees us and sends us while preserving us.
So, if you have ever been in my life you will always be in my life. God will sort it all out at the Bema seat (judgment for believers) and the White Throne (Judgment for unbelievers). As for me I'm not here to judge anyone. I'm just here to love people.
Jesus' life and words will separate the sheep from the goats in the end anyway.