Hm... but in my example, in order for the Church to do that, they would have to formally excommunicate that individual. That isn't something done often, and doesn't really support what you seem to be saying it does (unless I misunderstand you).
The Church doesn't get to just point at a person who commits a sin and say that person isn't a Christian. There is a formal process for evaluating if that individual meets certain criteria (laid out in scripture). Its not done without serious consideration.
And there is a significant difference between saying that a person "isn't a Christian" and saying that some practice by a christian "doesn't represent Christianity".
For a practice to be considered "Christian" it should resemble the established and agreed upon tenets of the Christian faith, as laid out in the Bible and generally agreed upon by the Church at large.
Its like, I can claim to be a lawyer, but to actually be one, I need to pass the Bar. And a lawyer can be disbarred, if their actions show them to unable to execute the duties of a lawyer in accordance with the standards set by the state they practice in.
Similarly, a licensed Lawyer can claim something is lawful, but that be false when compared to the actual written code of that state. Someone can then come along and say that the advice and practice of that Lawyer does represent the actual law of that state.
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Look, I get it. Its frustrating to see christians do bad things, and for the church to not take responsibility when it should. And I'm not defending that. It is also frustrating for the Church when people do not represent it fairly. This is a common issue with any organized group of people, because People aren't always reliable. A fact the Bible has much to say about.