Bingo! That is clearly the message many Christians take from Jesus, consciously or unconsciously.
I do lean toward that liberal view, as you suggest, and completely agree it is "unnatural" in the sense no human can love more than a limited circle of humans. (In "Schindler's List" Schindler at the end regrets not saving more Jews.) Perhaps Jesus meant "do what good you can." I used to be an altar boy, but have no idea whether God exists or not, and just try to be kind to people around me.