OK, I guess I've read enough stuff here, and in a bazillion other threads, about Christians, and what various people think makes a Christian, much of which makes me very sad. So, as a Christian (one flavour thereof), I have to respond.
[1] Simply stated, a Christian is someone who wants to be a follower of Christ, and to live as close as possible to the standard of love for one another and all things that he set. We aren't Christ, so we can't do it perfectly, and when we screw up, we are forgiven. And that, I think, is what that slogan is about. I don't particularly like the way it excludes people of other persuasions who are trying just as hard.
[2] There are many flavours of Christian, because we weren't around when he was, so there's a degree of interpretation required when discerning just what those standards are, and how to live them. Some are inclined toward a literal interpretation of the writings available to us, and take the Word in the Bible as literally written by God. Others try to study the societies in which those writings came to be, to understand how those circumstances might differ from today's, and therefore what remains literally relevant, and what is now symbolic. And there are many variations in between. None of us can know for sure, but what matters is that we try.
[3] Some wear their Christianity "on their sleeve", others prefer a more subtle statement, based solely in how they live their lives. My interpretation of a business's claim to be Christian is that it is run by someone of the former persuasion, who wants to let people of the same persuasion know that their values are observed by this business -- that they are "safe" doing business with this company. And also, to let people of other persuasions know that there is a standard observed here, which they believe to be desirable, but acknowledge others may have difficulty with for whatever reason. It's really just being up front with people, so they can decide whether this is a business they want to patronize.
[4] In any subset of humanity, you will find good and bad. Once born into a particular subset, one needs to be significantly disillusioned with it, in order to reject it, and stop identifying with it on at least some level. And there will always be people, born into a particular subset, who, while they don't entirely espouse the beliefs of that subset, find the label convenient. Some of those are still good people, others less so, unfortunately. But that is a condition of humanity -- not of Christianity. It applies, as does everything else I have said here, equally to any other religion, ethnic group, or other subset of humanity.
[5] Christians believe that Christ came to us both to show us God's love, and to atone for our sins. I have no idea what awaits me when I shed this body; I am confident that whatever it is will be orchestrated by a good and loving God, who loves all those other subsets just as well as he loves me, because he is also their God -- they just use a different name, and sometimes their interpretation differs somewhat from ours, but by and large, they are trying just as hard as we are to live decent lives.
[6] Christ said "Let he who is without sin, cast the first stone." I do wish we could all follow that -- me, too -- I don't always get it right, either.
So, there are some thoughts. Completely uncharacteristic for me to be so public, so I will just leave them with you.