IMO the only thing that is going to save anyone, is having a good kind heart.
I reckon the ones Jesus turns away are the ones who don't have that, never mind how much they might believe and use the name of Jesus.
To me that says if Christianity was right, it isn't just belief in Jesus that would save you, you need a kind heart.
That's how I read it.
I don't go a lot on the terminator Jesus, of the hell fire preachers.
Jesus does not turn anyone away: some turn away from Him. You need a kind heart, yes, but you need to demonstrate that by caring, and "doing," and having faith in Jesus to be "saved."