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I think that we should also consider the fundamentality of the problem at issue.

Let's suppose that we are thinking about interfering with some action X practiced by people in a group who do not accept our principles. Let's also suppose that we are judging this action by our principles. So we are assuming some sort of "appraiser's group relativism" at this point. Doesn't it matter whether X is a fundamental violation of our code or something of lesser importance? 

Let me clarify this with an example. Forcing women to kill themselves when their husbands die is a violation of what we consider a fundamental right. Forcing women to cook dinner for their husbands is not. Surely we stand a better chance of justifying interference to stop the former. So the fundamentality or gravity of the action we may interfere with is relevant when we are trying to justify interference.