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I think I can safely say that there are important cases when unplayed strings should not be touched with the fingers of the left hand.
For instance, playing G on the D string: if you touch the G string at the same time, you can't hear the G string's sympathetic vibration, and you deprive yourself of a very useful reference for precise intonation. And if you barely touch the G string in that case you will get a buzzing sound. I believe the audience can hear those effects also. It's the same when using the fourth finger to play D on the G string: touching the D string would mute its very strong resonance.
Can people name more cases when unplayed strings shouldn't be touched?
What are some cases when it doesn't matter?
What are some examples when it's necessary or desirable or convenient?