Question: What does *but until* in a sentence mean? I came across the phrase in a sentence that sounded almost exactly as this:

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> He was a great person **but until** he started caring for other people's feelings.
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I have found another example of sentence, tweeted by Rupert Murdoch. His tweet was:

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> Maybe most Muslims are peaceful, **but until** they recognize and destroy their growing jihadist cancer they must be held responsible.
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A compact explanation to this tweet would be real handy.

Answer: 
There is no phrase "but until". There are two words, *but* and *until*, which can be looked up in a dictionary.

Your second sentence could be rephrased as "Maybe most Moslems are peaceful. However, until..."; the main verb is *must be held*.

The first sentence is ungrammatical. If you have remembered it correctly, the writer mistakenly inserted "but" or (more probably) omitted "not"; you should remember that many writers are in a hurry on the Internet, and typos, infelicities and even grammatical errors do occur (even, occasionally, on EL&U).
The sentence is badly structured.

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> Maybe most Moslems peaceful, but until they recognize and destroy their growing jihadist cancer they must be held responsible."
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Paraphrase:

* It is possible that most Moslems are peaceful.
* Most Moslems [refuse to] recognize and destroy their growing jihadist cancer.
* [Therefore] most Moslems must be held responsible [for...*something*].
* When most Moslems recognize and destroy their growing jihadist cancer, then they don't have to be held responsible [for...*something*]

This doesn't make a lot of sense, obviously.