However, your quotes overlook what Jesus said about who will be saved: Matthew 25.
Then the king will say to those at his right hand, 'Come, you that are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world; for I was hungry and you gave me food, I was thirsty and you gave me something to drink, I was a stranger and you welcomed me, I was naked and you gave me clothing, I was sick and you took care of me, I was in prison and you visited me.' Then the righteous will answer him, 'Lord, when was it that we saw you hungry and gave you food, or thirsty and gave you something to drink? And when was it that we saw you a stranger and welcomed you, or naked and gave you clothing? And when was it that we saw you sick or in prison and visited you?' And the king will answer them, 'Truly I tell you, just as you did it to one of the least of these who are members of my family, you did it to me.'
sounds like some of them who are getting let into heaven don't even know Jesus personally, but he left them in anyway.
The passage says, "the least of my brothers."
That isn't particularly significant, but idea is about those who help "brothers of Jesus", even the least significant of them.
Let's say, Doc, that I help your family BECAUSE I've heard of you. In short, I am identifying with you. That means I'm SIDING with you.