Good question tracks.
I hate to say it, but I've seen many and many a professed believer who was abusive, dishonest, etc. I've also seen many quite honest and ethical non-believers. [There are entire congregations, for example, which tacitly support wife-beating, on the hideous grounds that it is necessary to compel the wife's 'submission' to her husband.] So I don't make distinctions based on the faith the individual professes, but rather on the behavior the individual exhibits - the fruits they bear, if you like.
That being said, if I'm dealing with an ethical person who is also a Christian, I will approach them on both ethical and Christian grounds, if I think they care and would accept being approached.
If I'm dealing with an ethical non-Christian, I will approach them on ethical grounds, and if they react positively, especially if they react with surprise as well [at my being reasonable], I may then have an opportunity to share how my faith has clarified this issue for me.
If I'm dealing with people whose behavior has consistently demonstrated or suggested a lack of ethics, a lack of insight, or both, and no empathy, it doesn't matter to me what they claim to believe.
In re the non-believer to believer, I have been approached by non-Christians when I've been thoughtless or slighting towards them. In the cases I'm thinking of, their concerns were valid, and I heard them and apologized and did my best to mend my ways. In one case I was upbraided for slighting someone when I claimed to be a Christian, and I had to agree that the person was absolutely right, I wasn't living up to what I claimed to believe. This person's expression when I admitted this was amazing - clearly they had a chip on their shoulder about Christians, and clearly in the past they had not been heard and responded to... at this point, I think they see me as a 'special case', which is sad, because I just think they have been damaged more by phonies, so their count is off.
I don't know if this helps, but it's where I am on the matter. My bottom line is this: If I'm dealing with people whose behavior has consistently demonstrated or suggested a lack of ethics, a lack of insight, or both, and no empathy, it doesn't matter to me what they claim to believe.
I tend to come down more on the side of C.S. Lewis and George MacDonald, on this. I think God makes prizes of many whose presence in our future life will surprise us [e.g., Nebuchadnezzar and Cyrus]... because only God knows the true heart and true beliefs of anyone. We can go by the fruits we see, but that mostly helps us avoid the most obviously dishonest. It doesn't help us determine what the honest may, deep in their hearts, sometimes in a place where they have no words for it, actually believe.