Many Christians will tell non-believers one thing to their face but say something else behind their back: during family dinners, prayer circles, or church coffee hours.
“Well, at least Mary is a very good person. I only wish she knew the Lord.” May be the start of a conversation during one of those coffee hours. And a reply her more doctrinally-informed friend could be “but Mary’s righteousness is like filthy rags without Jesus in her life.”
This reasoning comes from Isaiah 64:6 (KJV):
But we are all as an unclean thing, and all our righteousnesses are as filthy rags; and we all do fade as a leaf; and our iniquities, like the wind, have taken us away. (Composed immediately after exile in Babylon)
Interestingly, this verse comes from the Hebrew Bible — “the Old Testament” of Christians — “old” because it was replaced by a new Gospel of total forgiveness by the human-god sacrifice of Jesus. But the Hebrews, in Isaiah’s time, most likely had no refined doctrine of human sacrifice for sins (only animals), they had no hell and no devil either. Instead, to Jews back then, we were all in the same boat — well, unless you were a slave or a woman or …. With Christianity came the concept of true belief, of lost and the found, the saved and the unsaved, us vs. them. This is what makes some Christians whisper behind your back. So the correct Christian horrible answer is: No, without Jesus you can’t be good.
Triangulations 
Is there a distinction though between being “good” and being “saved?” I think there is an argument for that. Mary in you example can be “Good/Unsaved” whereas those in the kaffe-clutch are “Good/Saved?” Or does salvation cause a transubstantiation of “good” somehow? I don’t think that would be a doctrinal answer, but maybe a human one? My “Saved/Good” is more good than your “Unsaved/Good?”
@qbit: indeed, there is a tension among Christians themselves on this issue. Christians are encouraged to confess that they are sinners and always sinning. But the Holiness movement emphasizes the purification from sin. And many Christians belief that nonChristians may do “good” but unfortunately because they don’t have Jesus in their hearts, it can’t be lasting or eternal good. The us vs. them thinking is sly and often sneaks in one way or another. Did I address your point?
If only one were to read on in Isaiah (until the end of the book) they’d realize Gods anger is about false worship and hypocritical religious service, not about “not believing” in Him. IMO it is extremely silly and immature to believe someone is “good” or “can be saved” with mere belief alone that isn’t coupled with clear distinct action. If Christians want to believe in this , then go ahead. But leave Tanakh, what they call the Old Testament, out of it.
@ NZL: I agree that “beliefism” is silly: As I’ve written here. https://triangulations.wordpress.com/2013/08/06/beliefianty-beliefism/ . But a “god” being angry about false worship seems silly too. But then, most people’s anthropomorphic gods seem very odd to me.
I guess, that depends on how one defines “a good person”. “By their deeds shall you know them”. What are the deeds, that set Christians apart from the rest of us? Going to mass, prayer perhaps? Are those cultural requirements set for a virtuous person in the Christian mind set?
@rautakyy: Indeed, see my chart here where I show how Do-isms and Believe-isms address the issue you point out. https://triangulations.wordpress.com/2018/12/18/belief-isms-vs-do-isms/